VISUALIZING DYNAMIC QUANTITATIVE DATA IN HIERARCHIES

TimeEdgeTrees: Attaching Dynamic Weights to Tree Edges

Michael Burch and Daniel Weiskopf

VISUS, University of Stuttgart, Stuttgart, Germany

Keywords:

Hierarchy visualization, Time-series data.

Abstract:

In this paper we introduce a technique for visualizing the dynamics of quantitative data in static hierarchical

structures. We exploit the straight links of orthogonal tree diagrams as a timeline on which we visually encode

dynamic quantitative information. We use color coding and varying thicknesses to represent the time-varying

data. Bimodal data can also be displayed by exploiting both sides of the time axes simultaneously. Our

TimeEdgeTrees tool allows us to explore dynamic quantitative data in tree diagrams by interactive data ﬁlter-

ing and zooming. The spatial proximity of neighboring hierarchically structured elements allows us to easily

explore trends, countertrends, periodicity, temporal shifts, or anomalies during the evolution synchronously.

Interactive features such as expanding or collapsing of subhierarchies additionally help to detect the afore-

mentioned phenomena on different levels of granularity. The usefulness of our visualization technique is

illustrated by water level data acquired at more than 450 measurement stations along German rivers for 768

points in time.

1 INTRODUCTION

The most common visual metaphors for representing

hierachical kind of data are node-link representations

that encode the hierarchical objects as some kind of

circular or rectangular glyphs and the parent-child re-

lationships as links connecting the related hierarchical

elements. There are alternative approaches that avoid

explicit links, e.g., layered icicle diagrams (Andrews

and Heidegger, 1998; Stasko and Zhang, 2000; Yang

et al., 2003), tree-maps (Shneiderman, 1992), or in-

dented outline plots (Burch et al., 2010).

All these diagrams have more or less proved to be

useful for visually encoding static hierarchical data.

These are able to show parent-child relationships in

a single view and additional quantitative information

by color coding of nodes or sizes of rectangular boxes

as it is typical for tree-map representations.

In this paper, we focus on the problem of com-

paring dynamic quantitative data for all hierarchi-

cal entities—inner nodes as well as leaf nodes—

simultaneously. We introduce a representation where

each link of an orthogonal node-link tree diagram is

divided into as many segments as are necessary to dis-

play the different time steps in the hierarchical data.

Color coding and varying thicknesses are used to vi-

sually distinguish differently evolving branches in a

tree over time.

With our diagrams we intend to explore dynamic

quantitative data in a hierarchy for the following be-

haviors on different levels of granularity:

• Trends. Quantitative information behaves sim-

ilarly for a group of hierarchical entities, that

means, the metric for all entities shows a grow-

ing or shrinking behavior in the same or a nearly

similar way in the same time interval.

• Countertrends. Quantitative information be-

haves differently or even in opposite direction for

a group of hierarchical entities in the same time

interval.

• Periodicity. The data shows some kind of peri-

odic behavior: there are repeating patterns in the

time-varying data with the same period length.

• Temporal Shifts and Scale. The dynamic quanti-

tative data shows the same characteristics for cer-

tain hierarchical entities but with a temporal dis-

tance or at a different scale.

• Anomalies. There is some kind of strange or un-

expected behavior in the dynamic data such as

missing data points or values outside a trend be-

havior.

The most natural way to visualize time-series data

177

Burch M. and Weiskopf D..

VISUALIZING DYNAMIC QUANTITATIVE DATA IN HIERARCHIES - TimeEdgeTrees: Attaching Dynamic Weights to Tree Edges.

DOI: 10.5220/0003323901770186

In Proceedings of the International Conference on Imaging Theory and Applications and International Conference on Information Visualization Theory

and Applications (IVAPP-2011), pages 177-186

ISBN: 978-989-8425-46-1

 2011 SCITEPRESS (Science and Technology Publications, Lda.)

is by mapping the dynamics of the data to time that is

represented by an animated sequence of diagrams. In

general, it is difﬁcult for human viewers to remember

all visual properties of all elements in an animation

because of their limited short-term memory (Ware,

2008). As a possible solution to this problem, they

might have to let play the animation several times

until they understand the dynamic data. Visualizing

the hierarchical organization of the dynamic data in

the same animation increases the cognitive load for a

viewer immensely.

To overcome these problems we use a static rep-

resentation of the time-series data instead. To allow

better exploration of the visualized data, interaction

methods can be applied to the visualization to browse

through large data sets with high complexity of the

hierarchy or a large number of time steps. As addi-

tional features, the dynamic quantitative data can be

shown in a bimodal fashion or in a logarithmic scale.

Representing all these visual dimensions at once is at

least very difﬁcult or even impossible in animated di-

agrams.

We show the usefulness of the visualization

technique by visually exploring a data set from

a web site that contains time-varying water level

data (PEGELONLINE, 2010). We requested water

level data for 768 points in time at more than 450

measurement stations along German rivers.

2 RELATED WORK

The TimeEdgeTrees visualization is inspired by or-

thogonal node-link diagrams for representing hierar-

chies. The main beneﬁt of those diagrams is that

they already contain straight links that are exploited

as timeline representations.

2.1 Static Hierarchy Visualization

In general, there is a huge body of previous research

on the visualization of static hierarchies (McGufﬁn

and Robert, 2009). For instance, (Battista et al.,

1999), (Herman et al., 2000), and (Reingold and Til-

ford, 1981) use conventional node-link diagrams to

depict relationships between hierarchically ordered

elements. Several variations exist for node-link rep-

resentations that make use of differently oriented di-

agrams. Attaching an attribute to all of the nodes—

for example a text label—using node-link diagrams

may lead to overlaps in the display and visual clutter.

Moreover, a simultaneous comparison of all attributes

is problematic since these are not aligned in the same

way in such a diagram. A similar problem occurs

when showing quantitative information for each of the

nodes in the diagram.

Radial node-link approaches organize tree nodes

on concentric circles, where the radii of the circles

depend on the depths of the corresponding nodes in

the tree (Battista et al., 1999; Herman et al., 2000;

Eades, 1992). On the one hand, this technique leads

to a more efﬁcient usage of space; on the other hand,

it is more difﬁcult to judge if a set of nodes belongs

to the same hierarchy level. This apparent drawback

of radial diagrams can be explained by the fact that

the human visual system can judge positions along a

common scale with a lower error rate than positions

along identical but non-aligned scales, as demon-

strated in graphical perception studies by (Cleveland

and McGill, 1986). Balloon or bubble tree layouts are

another strategy to display hierarchical data as node-

link diagrams: they represent the hierarchical struc-

ture in a clear way but do not scale for large and deep

trees (Herman et al., 2000; Grivet et al., 2006). As

another drawback, it is difﬁcult to attach an attribute

to each tree node for comparisons between hierarchy

levels.

Tree-maps (Shneiderman, 1992) are a space-

ﬁlling alternative for displaying hierarchies. One

drawback of tree-maps is the fact that hierarchi-

cal relationships between parent and child nodes are

hardly perceived in deeply nested hierarchical struc-

tures. Nesting can be indicated by borders or lines of

varying thickness—at the cost of additionally needed

screen space. Tree-maps are an excellent choice when

encoding quantitative data attached to hierarchy lev-

els. However, showing dynamic quantitative data in

the tree-map boxes makes comparisons between sin-

gle hierarchical entities difﬁcult. In many cases, the

tree-map boxes are scaled down to pixel-based graph-

ical elements and hence, a timeline representation is

not possible in a static tree-map.

Layered icicle plots require substantial amount of

image space: they use as much area for parent nodes

as the sum of all their related child nodes together. A

beneﬁt of this representation is that the structure of the

displayed hierarchy can be grasped easily and more-

over, this type of diagram scales to very large and

deep trees. Variations of this idea are known as Infor-

mation Slices (Andrews and Heidegger, 1998), Sun-

burst (Stasko and Zhang, 2000), and InterRing (Yang

et al., 2003). These diagrams make use of polar co-

ordinates, which may lead to misinterpretations of

nodes that all have the same depth in the hierarchy.

As another drawback, all icicle-oriented techniques

require separation lines between adjacent elements al-

lowing differences in hierarchy levels and nodes to be

perceived.

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178

Indented outline approaches (Burch et al., 2010)

can be scaled down to pixel-based and indented line

plots to represent the hierarchical structure. This ap-

proach has the beneﬁt that attributes can easily be at-

tached to all of the nodes in the represented hierarchy

and aligned to allow better comparisons. (Burch et al.,

2010) showed in a user study that indented outline ap-

proaches for visualizing hierarchies do not have sig-

niﬁcant beneﬁts over conventional rooted node-link

diagrams with respect to typical exploration tasks in

hierarchies but can be easily learned after a short ex-

planation time of just ten minutes.

2.2 Visualization of Timelines

Our approach is similar to the concept of sparklines

(Tufte, 1990). Sparklines show trends, countertrends,

periodic behaviors, temporal shifts, and also anoma-

lies of quantitative time-varying data, such as average

temperature or stock market activity, in a simple and

condensed way. A group of sparklines is often placed

close to each other as elements of small multiples. We

extend this concept by adding a hierarchical structure

to the set of sparklines that supports the exploration

of time-varying data on different levels of granularity

as well.

There exists only little work on the representa-

tion of dynamic quantitative data in hierarchies. The

TimeTree technique (Card et al., 2006) allows the user

to explore a changing hierarchy, encoding the infor-

mation about each element at each time step in the

corresponding node of the tree represented as a node-

link diagram. A time sliding function can be used to

interactively browse and search organizational hierar-

chies over time. However, only one static diagram

can be explored at a time. In contrast, the TimeEd-

geTrees can show the whole dynamic data or at least

a large portion of it in a static view, which preserves

one’s mental map of the data. (Tu and Shen, 2007)

use a different visual metaphor to represent changes

of hierarchical data. They introduce a new tree-map

layout algorithm to reduce abrupt layout changes and

produce consistent visual patterns.

The Timeline Trees technique (Burch et al., 2008)

and its radial counterpart TimeRadarTrees (Burch and

Diehl, 2008) make use of node-link diagrams attached

to a matrix-like representation that shows evolving

quantitative data in a timeline. Additionally, relations

are shown among commonly changed hierarchical en-

tities by a thumbnail view. The drawback of these di-

agrams is that timelines are only visible for leaf nodes

but not for inner nodes, and that they show the time-

lines in a different view than the hierarchy itself.

(Hadlak et al., 2010) describe a way to embed hi-

erarchies into regions of a map display by using a

point-based layout. The dynamics in the data is vi-

sually encoded by layering and animations.

3 TimeEdgeTrees

The TimeEdgeTrees approach relies on the oberser-

vation that the visual metaphor of node-link diagrams

for hierarchical data already contains straight lines

connecting related hierarchical elements. These lines

can easily be exploited as timelines to visually encode

the dynamics of quantitative data. Each link is divided

into as many segments as time steps have to be rep-

resented simultaneously. Additionally, each segment

is color coded with respect to the strength of the hi-

erarchical entity at the point in time. If the strengths

vary in some kind of exponential fashion, a logarith-

mic color scale can also be used to make the differ-

ences between smaller values more apparent. If the

user is interested in small and large deviations from

mean values, a bimodal color scale may also be ap-

plied. For this, we additionally exploit both sides of

each timeline.

3.1 Data Model

We model an information hierarchy as a tree T =

(V, E), where V denotes a set of vertex-function pairs

V = {(v

, f

), (v

, f

), . . . , (v

, f

)}

with f

: N −→ R. The set E ⊆ V × V contains

the parent-child relationships of the hierarchy. The

functions f

map discrete time steps to real valued

numbers—the quantitative data for each node v

each point in time. A single time step can be iden-

tiﬁed by a unique number j ∈ N, i.e. the set of all

discrete time steps {t

| 1 ≤ j ≤ n, j ∈ N} has a natu-

ral order.

We deﬁne the arithmetic means f

of some func-

tion f

in an interval [t

, t

] as

∑

j=l

( j)

m − l + 1

Later, we need f

to transform the representation into

the bimodal mode.

3.2 Encoding of Time-varying Data

The dynamic quantitative data is initially represented

in a color coded segmentation of each link depending

on the number of time steps.

Figure 1 shows an example of dynamic data vi-

sualization in an orthogonal node-link diagram. We

VISUALIZING DYNAMIC QUANTITATIVE DATA IN HIERARCHIES

- TimeEdgeTrees: Attaching Dynamic Weights to Tree Edges

179

Figure 1: An orthogonal node-link diagram with addition-

ally color coded timelines and varying thicknesses showing

21 time steps of dynamic quantitative data at each of the

links.

choose an orthogonal layout since the timelines on

each hierarchy level with the same depth are aligned

in a common scale; this layout is best suited when

judging and comparing differently sized rectangu-

lar boxes for each time step (Cleveland and McGill,

1986). Throughout this paper, we use color coding

by vegetation scale: smaller values are represented in

blue, larger ones in green to yellow, and the largest

ones in red. The timeline for a node v ∈ V always

starts where the corresponding link is entering the par-

ent node and chronologically leads to the respective

node v ∈ V .

Using color coding as the only visual feature

makes efﬁcient use of space, but as a drawback, indi-

vidual colors cannot be perfectly differentiated when

there are too many colors and when those are hardly

differing (Ware, 2008). For this reason, the TimeEd-

geTrees tool additionally supports visual encoding

by varying thicknesses to improve the perception of

weakly changing metric values when following a link

with the eye.

Figure 2 illustrates our approach for just one node

of a tree. In Figure 2 (a), we use color coding to

show the evolution of quantitative data over time.

Figure 2 (b) depicts encoding by varying thickness,

which makes differences in the single data points ap-

parent. Typically, we combine both features—color

coding and varying thickness—to encode dynamic

quantitative data because similar patterns in differ-

ently located tree branches can be better detected and

compared when visualizing the data in this way, see

Figure 2 (c). Furthermore, color coded diagrams are

aesthetically appealing.

The data can also be displayed in bimodal mode,

i.e., we divide the data values into two separate cat-

egories where each is displayed on one side of each

time axis. For the river level data, we ﬁrst subtract

the arithmetic means f

from all other values. Nega-

tive values are displayed on the left part of the time

axis and positive values on the right side. Figure 3 (a)

shows the same dynamic quantitative data as in Fig-

(a) (b) (c)

Figure 2: Different representations for dynamic quantitative

data: (a) color coding only; (b) varying thickness without

color coding; (c) combination of both.

(a) (b)

Figure 3: Dynamic data may also be displayed in (a) bi-

modal mode or (b) logarithmic mode.

ure 2 in the bimodal mode. One can see that the data

behaves differently on both sides of the axis. The bi-

modal mode has another advantage: the display space

may be used more efﬁciently and a bimodal color cod-

ing might additionally strengthen the visual appear-

ance of the diagram.

A logarithmic scale allows a comparison of the

quantitative data points even if they differ to a very

large extent. Figure 3 (b) shows an example of a log-

arithmic scale. One can easily see that there are only

small differences at the peaks and their neighboring

data points.

3.3 Node-link Layouts

Apart from orthogonal node-link layout, many other

layouts exist. In this section, we discuss the pros and

cons of them with respect to aesthetic tree drawing

criteria, space-efﬁciency, and the suitability for typi-

cal exploration tasks for this kind of data.

• Rooted Tree. The rooted tree diagram is the most

common way to visualize a hierarchy. The root

of the hierarchy is the topmost node in the rep-

resentation and the root nodes of the subtrees are

located on layers depending on the depth of the

subhierarchy in the tree, see Figure 4 (a). Rooted

trees can also be arranged from bottom to top,

from left to right, or from right to left.

• Orthogonal Tree. Using orthogonal bends for the

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180

(a) (b) (c) (d)

Figure 4: Node-link tree diagrams may be laid out in a variety of styles: (a) rooted tree diagram; (b) orthogonal tree diagram;

Table 1: Several criteria for the discussed node-link layouts (+ = good, o = average, - = bad).

Space- Comparability Hierarchy Exploration of

Technique Efﬁciency of Timelines Structure Deeper Levels

Rooted tree diagram - o + o

Orthogonal tree diagram - + o o

Bubble tree diagram - - o -

Radial tree diagram + - o +

links leads to an orthogonal tree diagram that is

best suited to compare the timelines of all hierar-

chical elements simultaneously, see Figure 4 (b).

• Bubble Tree. Another strategy to visualize trees

is by a bubble or balloon tree layout that recur-

sively represents subtrees on circles whose cir-

cle center lies somewhere on the circumference of

the circle representing the parent node, see Fig-

ure 4 (c).

• Radial Tree. A radial tree visualization positions

the root node in the center of a circle. Child nodes

on the same depth of the hierarchy are located on

circles with the same radius, where the radius lin-

early depends on the depth of each hierarchical

element in the tree, see Figure 4 (d).

Table 1 gives an overview of several criteria for

these node-link layouts and shows if a certain tech-

nique meets the criterion (+) or not (-) or if it cannot

be classiﬁed clearly (o). In this table, we brieﬂy sum-

marize four different criteria for visualizing dynamic

quantitative data in hierarchies by means of several

node-link layouts. Radial diagrams are the most

space-efﬁcient layout since trees normally grow ex-

ponentially with depth. The rooted tree layout is best

when exploring the hierarchical structure whereas or-

thogonal layouts allow for better comparisons of the

dynamic data since the timelines are aligned as com-

mon scales. The least useful type of diagram for this

visualization task is the bubble tree layout since there

the hierarchical structure is not as well expressed and

the smaller circular shapes for deeper trees lead to

timelines that are differing in length, orientation, and

scale. This again leads to problems when exploring

and comparing temporal shifts in the dynamic data.

3.4 Dynamic Behavior Analysis

As already discussed in Section 1, dynamic quanti-

tative data may show different behaviors for a list of

certain subhierarchies or hierarchical entities such as

trends, countertrends, periodicity, temporal shifts, or

anomalies. Figure 5 illustrates how the novel tech-

nique can be used to explore time-varying quantita-

tive data for these phenomena and for a group of hier-

archical entities at the same time.

In Figure 5 (a), all branches are evolving with the

same characteristic, hence, we would classify this be-

havior as a typical trend in dynamic data. Figure 5 (b)

shows that some hierarchical entities are evolving in

the opposite direction, a phenomenon that we would

classify as a countertrend with respect to the dynamic

data of other tree branches. In Figure 5 (c), there is

some kind of periodic behavior for all subhierarchies

in a similar way. The same pattern is reoccuring after

the same time interval again and again. Figure 5 (d)

shows that the same pattern or subpattern reappears in

all hierarchical entities but each after some delay. Fi-

nally, Figure 5 (e) shows an anomaly. Some branches

seem to evolve in a trend behavior whereas single

hierarchical entities are showing gaps in their time-

series data. Furthermore, some data points are miss-

ing or are error-prone.

In Section 4, we apply our technique to a data set

that contains water level data of German rivers. This

data set is well suited to explain all the behaviors of

dynamic data described above.

VISUALIZING DYNAMIC QUANTITATIVE DATA IN HIERARCHIES

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181

(a) (b) (c) (d) (e)

Figure 5: The dynamic quantitative data may show ﬁve different types of behaviors: (a) trends; (b) countertrends; (c) period-

icity; (d) temporal shifts; (e) anomaly.

3.5 Interactive Features

The visualization tool supports certain interactive fea-

tures that can be used to manipulate the hierarchical

data. Generally, we follow the visualization seek-

ing mantra of Ben Shneiderman: Overview ﬁrst,

zoom and ﬁlter, then details-on-demand (Bederson

and Shneiderman, 2003).

• Expanding and Collapsing of Subhierarchies.

By clicking on a node its corresponding subtree

is collapsed. If it is already collapsed it will be

expanded again.

• Selecting Speciﬁc Time Intervals. Only rele-

vant intervals in the evolution can be selected

and hence, the remaining time-varying quantita-

tive data can be represented in more detail.

• Weight Filtering. To support the viewer in com-

paring the quantitative information, only those

line segments are color coded that lie in between

the selected weight interval. All other values are

grayed out.

• Geometric Zooming. The tree diagram can be

scaled up/down by mouse drag and drop.

• Apply Color Coding. Different color codings can

be applied and tested if explorative tasks become

easier.

• Thickness Slider. The thickness of line segments

can interactively be changed.

• Labeling. To minimize visual clutter, text labels

can be represented in a vertical or horizontal ar-

rangement or as some kind of spiral representation

around each corresponding node.

• Details-on-Demand. Moving the mouse cursor

over a node or a timeline gives additional textual

information about the object in focus.

4 APPLICATION EXAMPLE

To show the usefulness of our novel technique we

applied it to a data set that contains the water levels

of more than 450 measurement stations at the larger

rivers in Germany. The river system itself is a good

example of a naturally structured hierarchy formed

by natural processes over several thousand years. A

measurement of the water level is taken every hour in

the time period from September 3rd, 2010 until Oc-

tober 4th, 2010. A simultaneous representation of all

water levels at each point in time with an additional

hierarchy is very difﬁcult but can give many insights

about the behavior of the water level movements and

the water level minima and maxima over time.

4.1 Dynamic River Tides

The measurement stations are ordered from left to

right with respect to their location at the river. The

stations are ordered starting with the one closest to the

source and ending with the one closest to the mouth

into a larger river or into the sea. If a smaller river

ﬂows into a larger one its subhierarchy is visually dis-

played between the corresponding measurement sta-

tions. This spatial proximity allows us to explore if

the water levels of river subsystems inﬂuence the wa-

ter levels of the larger rivers or vice versa.

Figure 6 presents an overview of the whole data

set in an orthogonal tree layout. We use a vegeta-

tion color scale to distinguish the water levels at each

point in time. The more red a color is the higher is the

water level at this point in time. Green color means

normal water level and blue color indicates that the

water level is below normal. Points in time where no

data is available are grayed out. Since the values often

differ to a high extent we initially apply a logarithmic

color scale.

The ﬁrst observation that one can make from Fig-

ure 6 is the hierarchical information that is explicitly

given by the orthogonal diagram. The root level ex-

presses that all rivers ﬂow into one of several possible

seas; that information can be obtained by inspecting

the three elements at the ﬁrst level of the hierarchy—

the North Sea, the Baltic Sea, and the Black Sea.

Even if this diagram hides most of the details,

it may let us observe some interesting phenomena.

Some of the water levels show periodic behavior. This

phenomenon is the result of the heavy tides of the

North Sea, which have a period length of approxi-

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Figure 6: A visualization of dynamic water level data of the larger rivers in Germany and their hierarchical structure can give

interesting insight in the evolution of the water behavior on different levels of granularity.

mately twelve and a half hours. Even the times and

amplitudes of the tides at the measurement stations

differ, from time to time, which depends on the com-

bined effects of the gravitational forces exerted by the

moon and the sun and the rotation of the earth.

Some subsystems show a pattern that crosses each

measurement station with a temporal shift. This is

apparently visible for the rivers Elbe on the left hand

side and the river Rhine close to the center of Figure 6.

A detail-on-demand request for the river Elbe shows

that the water level near the city of Dresden is more

than four meters above normal height. The temporal

shift shows that the cities and villages downward the

river have to be aware of high watermarks and ﬂood-

ing in the near future.

For Figure 7, we ﬁlter the river hierarchy for the

river Rhine and all of its conﬂuents, which include

the river Neckar, the river Main, the river Lahn, and

the river Mosel, which again has a conﬂuent, the river

Saar. We can easily see that there are 24 main mea-

surement stations along the river Rhine. Around the

26th of September, there is a larger ﬂood wave above

the normal water level at the measurement station If-

fezheim. In the next days, the ﬂood wave is passing

VISUALIZING DYNAMIC QUANTITATIVE DATA IN HIERARCHIES

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183

Figure 7: A visualization of the water level data for the river Rhine can uncover interesting phenomena: waves with different

amplitudes are crossing the measurement points with a temporal shift and their amplitude shows a decreasing behavior.

Figure 8: A representation of dynamic water level data for the river Elbe shows different behaviors: one big wave is crossing

the measurement stations near the source of the river, whereas the measured data at the mouth to the North Sea shows periodic

behavior because of the large tides there.

the other stations subsequently but is weakening over

time. This can be detected by inspecting the changing

color from an orange color over yellow into a yellow-

ish green.

The conﬂuents of the river Rhine do not show

this large ﬂood wave behavior apart from two ex-

ceptions. The stations Lahnstein-UW and Koblenz-

Luetzel-DFH can be classiﬁed as anomalies. Al-

though the water levels are low overall, these two

measurement stations have high water levels. A closer

look at the hierarchy reveals that the rivers Lahn and

Mosel are converging there into the river Rhine and

hence, are above normal all the time.

Another interesting water level behavior can be

seen at the river Elbe, see Figure 8. Here, we ap-

plied the bimodal mode that makes use of both sides

of the time axes. The left hand side represents wa-

ter levels below the normal level, whereas the right

hand side shows the water levels above the normal

water level. The measurement stations seem to fall

into two categories if we inspect the left and the right

parts of the ﬁgure in more detail. Again, the yellow

color and the larger thickness on the right hand side of

each axis give us the insight that a ﬂooding is cross-

ing each of the stations over time. If we have a closer

look at the data visualized for the ﬁrst ﬁve measure-

ment stations, we can easily see that the amplitude at

the beginning of the ﬂood wave color coded in yellow

remains constant and only the wave’s length is grow-

ing. The ﬂooding has not reached the measurement

stations near the mouth to the North Sea.

The second category of dynamic data behavior can

be seen on the right hand side of Figure 8. The data

values show periodic behavior caused by the high and

low tides of the North Sea and the spatial proximity

of the measurement stations to the North Sea.

Figure 9 (a) shows that even the high and low

tides differ with respect to the size of their ampli-

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184

(a) (b)

Figure 9: The tides of the North Sea show some kind of periodic behavior and: (a) the amplitudes of high and low tides are

also changing; (b) temporal shifts can be detected when just showing dynamic data for one and a half day.

tudes from time to time. Furthermore, a temporal shift

in the wave pattern can be detected easily, see Fig-

ure 9 (b). Interesting is the fact that the station Ham-

burg St. Pauli has the highest tides even though the

station is the furthest away from the North Sea among

all the stations with periodic water level behavior.

5 CONCLUSIONS

In this paper, we demonstrated how the visual

metaphor of node-link diagrams may be used to dis-

play a hierarchy with additional dynamic quantitative

data. Straight links that encode parent-child relations

can easily be interpreted as a timeline starting at the

parent node and ending at the child node. The link is

divided into as many line segments as time steps have

to be visualized. Color coding is used to show the

strength of the hierarchical entities for each time step.

We conjecture that using orthogonal layout is best

suited for representing this kind of data since only

there the timelines in each subhierarchy are aligned

and hence, allow for direct comparisons of dynamic

data between single hierarchical entities. Possible al-

ternative layouts such as the traditional rooted tree

from top to bottom, radial diagrams, and bubble trees

have also been discussed.

We have applied the technique to a data set that

contains water level data for German rivers acquired

between September 3rd, 2010 and October 4th, 2010

at more than 450 measurement stations.

The visualization tool supports interactive features

such as expanding or collapsing of subhierarchies,

selecting time intervals, weight ﬁltering, details-on-

demand and the like.

In the future, we plan to apply the tool to differ-

ent application domains, for example software evolu-

tion data and we also plan to evaluate the visualization

technique by a user study.

ACKNOWLEDGEMENTS

We would like to thank Pegelonline (PEGELON-

LINE, 2010) for providing the river level data set.

This work was funded by DFG as part of the Prior-

ity Program “Scalable Visual Analytics” (SPP 1335).

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