Research Note: Sankey diagrams for visualizing land cover

dynamics

Nicholas CUBA 1

1 School of Geography, Clark University, 950 Main St., Worcester, MA, 01610, USA;

ncuba@clarku.edu; Tel.: +1-508-793-7336; Fax: +1-508-793-8881

Landscape and Urban Planning, 139, July 2015, 163-167

doi:10.1016/j.landurbplan.2015.03.010

ABSTRACT: Comparison of categorical maps from two or more points in time is a common

technique to detect land cover and land use change. Cross-tabulation matrices, which contain

information on the sizes of categorical differences between two maps, are often used to describe

the amount and type of land cover change that has occurred between two points in time. However,

the use of multiple matrices to describe changes occurring over more than one time interval can

be difficult to interpret. This article presents a graphical method for presenting the land cover

information contained in one or more cross-tabulation matrices based on Sankey diagrams, which

depict the flow of energy or materials through a network. Through the example of a series of land

cover maps of the San Juan, Puerto Rico area (1999-2003), this form of Sankey diagram is

demonstrated to efficiently and elegantly present information on land cover persistence and change

over multiple time intervals.

1. Introduction

Comparison of categorical maps from two or more points in time is a common technique

to detect land cover and land use change. Cross-tabulation matrices, in which each row is a land

cover category at time t0, each column is a land cover category at a subsequent time t1, and each

entry is the area experiencing land cover change or persistence during the interim between t0 and

t1, are widely used to facilitate map comparison (see Figure 3; Lewis & Brown, 2001; Pontius &

Cheuk, 2006). These matrices usefully communicate precise quantities related to a map of

change, and metrics derived from diagonal and non-diagonal entries, and from row and column

totals, in the cross-tabulation matrix can indicate rates of change in a landscape, and the

prevalence of certain categorical transitions (Aldwaik & Pontius, 2012; Han et al., 2009).

However, when it is desirable to track the amount or intensity of land cover changes over more

than one time interval, reliance on the use multiple tables to compare maps can yield an

inefficient and difficult to interpret presentation of results when compared to graphical figures

(Runfola & Pontius, 2013).

In particular, new methods for communicating and visualizing land change dynamics are

needed in response to recent advances in the remote sensing of land systems that track fine and

moderate resolution change using temporally dense image stacks (see Kennedy et al., 2010).

These advances, made feasible by free distribution of Landsat data (Wulder et al., 2012) and

expanded processing of global imagery (USGS, 2013), allow for the identification and analysis

of discrete land change drivers and their impacts in functionally diverse land systems. Such

methodological innovations will be useful for work toward several central issues in land change

science, such as illuminating processes of land use competition, and identifying distal drivers of

change in a landscape or telecoupled systems (Munroe et al., 2014).

Methods of visual representation are central to landscape planning and analysis, allowing

for easier involvement of non-experts in these processes (Lange, 2011; Orland, 1994) and

serving to highlight the form or scale of underappreciated phenomena or interactions among

actors (Bebbington et al., 2014). Visual clarity in the presentation of baseline or predicted

scenarios can enhance community engagement efforts, and communication between researchers

and practitioners (Pettit et al., 2011). Techniques such as image segmentation and color shading

are used to highlight the spatial and temporal patterns of fine-scale changes in a map (see e.g.

Zhu et al., 2012). This article presents an easy to interpret format for depicting the summary,

broad-scale land cover dynamics information contained in one or more cross-tabulation matrix

using Sankey diagrams.

Sankey diagrams depict flow to and from various nodes in a network, and have been most

typically applied to analysis of energy or material flows (Schmidt, 2008). Arrows or directional

lines are used to represent these flows, with the thickness of the arrow or line proportional to the

magnitude of the flow. These diagrams are commonly employed in Industrial Ecology to depict

product life cycle assessments, and in engineering to visualize quickly energy efficiency

(Schmidt, 2008).

Sankey Diagrams give emphasis to the size and direction of flows within a system, and

because of their broad utility have been applied in many geographic or human-environment

research contexts. Sankey diagrams’ utility for tracing material flows has made them illustrative

tools for the analysis of food systems (Courtonne et al., 2012), greenhouse gas emissions

(Bachmaier et al., 2010; Schnitzer et al., 2007), and water resources (Curmi et al., 2013).

Although the application of Sankey diagrams to land cover change research described here is

novel, the role of land change as a driver of increased atmospheric CO2 has featured in some of

the better known examples of the diagram, which trace the relative proportions of global

greenhouse gas emissions originating from various source sectors or activities (see Herzog,

2005).

2. Data and Methods

This paper examines land cover maps of the Río Piedras River Watershed and environs in

the San Juan, Puerto Rico area using 30 m spatial resolution maps from 1999, 2000, 2001, and

2003 (Fig. 1). The year 1999 and 2003 maps were produced at spatial resolution of 15 m and

were upscaled to 30 m and assigned the pixel majority/plurality category. Each map has a

different institutional origin, produced in order to further diverse applications and using different

methods (Gould et al., 2007; Helmer & Ruefenacht, 2005; Homer et al., 2004; Lugo et al., 2011).

Originally, each map used between 10 and 70 land cover categories prior to category aggregation

undertaken to facilitate comparison, which attributed all pixels to one of six semantically broad

categories, e.g. Barren, Built, Forest, Grass/Shrub, Water, and Wetland. Although substantial

variation in map production methods and semantic differences in category taxonomy that persist

after aggregation likely account for a non-trivial portion of difference between maps, these are

ever-present features of land cover mapping (Ahlqvist & Gahegan, 2005), and this set of maps

works well to illustrate the utility of Sankey diagrams for depicting differences between land

cover maps of the same area from multiple points in time.

In order to facilitate a discussion of this set of maps and the use of Sankey diagrams to

depict land cover dynamics, certain terms are defined. For a comparison of two categorical land

cover maps that use the same set of N categories, there are N * (N – 1) potential forms of map

difference, with each form consisting of pixels which are classified as category i in one map and

category j in the other map, where i does not equal j. In addition to map differences, there are N

instances of map similarity, or groups of pixels that are classified as the same category in both

maps. Map differences are typically regarded as land cover or land use change, while instances

of map similarity are typically regarded as land cover or land use persistence. Together, these

instances of persistence and change account for all entries in the cross-tabulation matrix, and

each is represented in the Sankey diagram by a persistence or transition line.

The Sankey diagram used here to visualize land cover dynamics in the area of the Río

Piedras River Watershed shows classification results from four maps, and the persistence and

change observed in three time intervals: 1999 to 2000, 2000 to 2001, and 2001 to 2003. Cross-

tabulation matrices that compare the two maps which bound each time interval are also

presented.

3. Results and Discussion

The presented Sankey diagram visualizes land cover category extent in the San Juan area

in four years, and persistence and change occurring from 1999 to 2000, 2000 to 2001, and 2001

to 2003 (Fig. 2). It is accompanied by three cross-tabulation matrices that list the category

extents in each year, the size of category persistence and transitions during the three time

intervals, and the gross gain and loss of each category (Fig. 3). Figure 2 is comprised of four

stacked vertical bars representing land cover within the study area in each of the four years for

which land cover maps were available, and three sets of persistence and transition lines

positioned between each chronologically sequential pair of stacked bars.

The stacked bars visualize the relative abundance of each land cover category in 1999,

2000, 2001, and 2003. The height of each component in the stacked bars is proportional to the

relative abundance of the represented land cover category in the study area, and categories are

arranged vertically by spatial extent, in largest-to-smallest order.

The category-level net map difference is easily interpretable from the stacked vertical

bars in the diagram (Fig. 2). The Built category is predominant in all four years for which there

are maps; comprising 63.1% of the total map area in 1999; 71.9% in 2000; 74.7% in 2001, and

64.6% in 2003 (Fig. 3). The Forest category and the small-extent Barren, Water, and Wetland

categories have relatively stable total extents throughout the four years. Finally, the spatial extent

of the Grass/Shrub category decreases in the intervals 1999-2000 and 2000-2001, but increases

in the interval 2001-2003. All four stacked bars have the same horizontal width, and for

diagrams that depict land cover dynamics over a high number of time intervals this width may be

reduced so that more of the diagram page space may be given to represent land cover persistence

and change during all time intervals.

Each of three sets of persistence and transition lines is positioned between the stacked

bars representing land cover maps of an initial time t0 and a subsequent time t1, connecting two

categories and representing land cover transitions from a category i at time t0, to a category j in

time t1, or persistence of category i at both times. The vertically-measured thickness of each line

is proportional to the size of the land area that experiences the corresponding persistence or

transition. The horizontally-measured length of lines vary in proportion to the length of the time

interval between the two compared maps. Thus the lines that describe differences between the

1999 and 2000 maps are the same horizontal thickness as the lines that describe differences

between the 2000 and 2001 maps, while the lines that describe differences between the 2001 and

2003 have twice the horizontally-measured length because they represent map differences and

similarities over a two year time interval. Each line is assigned the color of the initial category i

at time t0.

A vertical ordering scheme of stacked bars based on category spatial extent at each time

results in the persistence line of the largest category being placed at the top of the figure. Such a

placement for this typically large land cover persistence concentrates many of the smaller

persistence and transitions lines in the bottom portion of the figure.

Small-thickness, vertical white lines separate the stacked bars from persistence and

transition lines to demarcate clearly these diagram components. Figure 2 employs a slightly

darker color shade for persistence and transition lines than for category extents of the stacked bar

charts to further differentiate these component types. In order to reduce visual clutter in the

diagram, a threshold value may be chosen and applied to map persistence and transitions, such

that all lines smaller than the threshold are not depicted. Here, only lines of thickness greater

than 0.4% of the total map area are shown. A higher threshold value may be desirable due to

space considerations as the number of time intervals or categories examined increases.

The transition lines reveal high amounts of gross category-level map difference in the

face of relatively low net difference, particularly for the categories of Forest and Grass/Shrub

(Fig. 2). The net increase in the spatial extent of the Built category observed from 1999 to 2000

and from 2000 to 2001 is seen to be largely attributable to conversion of Grass/Shrub (Fig. 3;

7.3% of map from 1999 to 2000 and 5.2% from 2000 to 2001), and to a lesser extent Forest

(5.2% of map from 1999 to 2000 and 2.1% from 2000 to 2001). The presence of high gross

change in the absence of substantial net change may be indicative of cyclical land management

strategies such as crop rotation. In contrast, the presence of net increases or decreases involving

the same losing and gaining categories across multiple time intervals is evidence for broad-scale,

directional, and temporally persistent land change drivers.

The diagram highlights those categories that are dynamic in both absolute and relative

terms. The Grass/Shrub category extent is one such dynamic category, with large gross gains and

losses in category extent observed in multiple time intervals. The dynamic quality of this

behavior is visually evident from the low ratio of Grass/Shrub persistence relative to observed

Grass/Shrub category extent. Calculated using entries in the cross-tabulation matrices, the

proportion of Grass/Shrub persistence relative to the spatial extent of Grass/Shrub in the initial

year of each time interval was 0.29 from 1999 to 2000, 0.26 from 2000 to 2001, and 0.54 from

2001 to 2003. The proportion of persistence relative to the spatial extent of Grass/Shrub in the

final year of each time interval was similarly low: 0.40 from 1999 to 2000, 0.36 from 2000 to

2001, and 0.26 from 2001 to 2003. The relatively low ratios for Grass/Shrub contrast sharply to

the proportional measurements of a less dynamic category such as Built. Built persistence

relative to the spatial extent of Built in the final year of each time interval is 0.81 from 1999 to

2000, 0.88 from 2000 to 2001, and 0.96 from 2001 to 2003.

Sankey diagrams such as the one presented here complement the cross-tabulation matrix

as a means for conveying the size of land cover category extents at different times, and amounts

of change and persistence during the interim. Sankey diagrams might potentially be used as a

suitable replacement for these matrices if the size of all components of the diagram were

labelled. Such labels might not be able to be included in a static diagram due to limits on figure

space, but an interactive diagram can incorporate this information effectively in popup windows

prompted when the cursor hovers over related diagram components.

4. Conclusions

This paper presents a graphical method for presenting the land cover information

contained in one or more cross-tabulation matrices based on Sankey diagrams, which depict the

flow of energy or materials through a network. This form of Sankey diagram is easy to visually

interpret, and can efficiently convey land cover change over multiple time intervals.

Visualization of land cover dynamics using Sankey diagrams does not abrogate the usefulness of

presenting precise measurements of land cover dynamics in tabular form, but rather offers

benefits that complement those of cross-tabulation matrices. The example case of land cover

change in the area of San Juan, Puerto Rico, illustrates the potential for the visualization method

to depict net and gross change in category extent over one or more time intervals.

Acknowledgments

The author would like to thank the San Juan Urban Long Term Research Area project

(NSF: #BCS-0948507) for providing data, as well as two anonymous reviewers and Dr. Robert

Gilmore Pontius Jr. for providing feedback and encouragement.

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Figures

Figure 1. The land cover maps of the San Juan, Puerto Rico area used to illustrate the utility of

Sankey diagrams to depict map differences.

Figure 2. Sankey diagram for comparison of land cover dynamics in three time intervals defined

by four land cover maps from the years 1999, 2000, 2001, and 2003.

Figure 3. Cross-tabulation matrices for land cover maps from 1999, 2000, 2001, and 2003,

showing the extent of land cover category persistence and changes during the three time intervals

bounded by these years.