Star Plots

A star plot is a graphical method of displaying multivariate data with an arbitrary number of variables. Each variable is represented by a separate spoke, with each star representing a single observation. The length of each spoke is proportional to the magnitude of the variable for the data point relative to the maximum magnitude of the variable across all data points. A line is drawn connecting the data values for each spoke. This gives the plot a star-like appearance and the origin of the name of this plot.

Star plots can be used to answer such questions as: What variables are dominant for a given observation? Which observations are most similar, i.e., are there clusters of observations?
Are there any outliers?

The star plot observed above depicts crime rates as a function of 7 separate variables of major cities across the US.
http://www.math.yorku.ca/SCS/Gallery/images/starcrim2.gif

Correlation Matrix

A correlation is a single number that describes the degree of relationship between two variables. A Correlation Matrix lists the individual correlations between any two sets of variables.

To locate the correlation for any pair of variables within the matrix, you would need to find the value in the table for the row and column intersection for those two variables. correlation Matrices are quite similar to similarity matrices, except for that correlations have values ranging ONLY from -1 to 1, with -1 representing the least amount of correlation and 1 respresenting the greatest.

http://www.styleadvisor.com/products/styleadvisor/images/correlation3.gif

Similarity Matrix

A similarity matrix is a matrix of scores which express the similarity between two data points. They are used in sequence alignment: higher scores are given to more similar characters, and lower or negative scores are given for dissimilar characters.
Above is a similarity matrix of common amino acids. The similarity or dissimilarity of each amino acid pair can be found by finding the cross value of the two.

http://mendel.ethz.ch:8080/Server/ServerBooklet/_17545_tabular891.gif

Stem and Leaf Plot

A stem-and-leaf plot is a display, similar to a histogram, that organizes data to assist in visualizing the shape of a distribution. A basic stem and leaf plot contains two columns separated by a vertical line. The left column contains the stems (the first digit of a value) and the right column contains the leaves (the remaining digits of each value).

http://www.uow.edu.au/student/attributes/statlit/modules/images/2_50.gif

Box Plot

A Box Plot, also known as a box-and-whisker diagram, is an effecient method used for displayig 5-number data summaries. Box Plots summarize the following statistical measures: median, upper and lower quartiles, and the minimum and maximum data values. An example of a boxplot is shown below:

http://www.stat.sfu.ca/~cschwarz/Stat-201/Handouts/boxplot.png

Histogram

A histogram is a graphical display of frequencies, shown as bars. It shows what proportion of observations fall into each of several preset categories. A histogram differs from a bar chart in that it is the area of the bar that denotes value, not the height as in bar charts. The histogram above shows frequencies of exam scores, and the area under each segment is directly proportional to the number of scores falling into that category.
http://media.techtarget.com/digitalguide/images/Misc/iw_histogram.gif

Parallel Coordinate Graph

Parallel Coordinate graphs is a data visualization technique used in analyzing large sets of multivariate data. Each variable in the data plot is represented as its own Y Axis on the graph. A maximum point for each Y axis is selected, and they are scaled relatively to each other so that each variable takes up the same area in the graph space. Each line drawn represents a single observation as it relates to each variable. Lines are drawn across each variable for each observation.

The Parallel Coordiate graph above illustrates correlations in gene expression data for different species of drosophilia (fly genes).

http://www-vis.lbl.gov/Events/SC07/Drosophila/3DParallelCoordinates.png

Triangular Plot

A triangular plot is one in which, as its name suggests, displays three variables or data sets in the shape of a triangle.
The above triangular plot plots different soil textures on each side of the triangle and the composition of different soil types by percentages of each different texture within the triangle's center.


http://soil.scijournals.org/content/vol65/issue4/images/large/1038f2.jpeg

Windrose

A wind rose is a graphic tool used by meteorologists to give a succinct view of how wind speed and direction are typically distributed at a particular location. Presented in a circular format, the wind rose shows the frequency of winds blowing from particular directions. The length of each "spoke" around the circle is related to the frequency that the wind blows from a particular direction per unit time. Each concentric circle represents a different frequency, emanating from zero at the center to increasing frequencies at the outer circles.

The above windrose is for Seattle, Washington.

http://www.climate.washington.edu/windrose/Seattle-WindRose.jpg

Climograph

A climograph is a graphical depiction of the monthly precipitation and temperature conditions for a selected place. Precipitation is shown by the bar graph. A line graph depicts temperature.
Below is an example of a climograph for Memphis, Tennessee:

http://www.uwsp.edu/geo/faculty/ritter/images/atmosphere/climate/climographs/memphis.jpg

Population Profile

A population profile can be defined as a chart showing the number of people as a function of their ages for any given location. The above population profile illustrates the breakdown of population by age in the US for the years 1970, 1980 and 1990. Population profiles also for viewers to see changes in population distribution by age over time.http://www.co.nezperce.id.us/planning/comp_plan/1998_CPLAN/Fig9-3.jpg

Scatterplot

Scatter plots are similar to line graphs in that they use horizontal and vertical axes to plot data points. Scatter plots have a very specific purpose in that they show how much one variable is affected by another. The relationship between two variables is called their correlation .

Scatter plots usually consist of a large body of data. The closer the data points to making a straight line when plotted, the higher the correlation between the two variables and the stronger their relationship. Scatterplots should be constructed when the relationship between two variables is of interest.

The above scatterplot is interesting, as it plots the age of husbands versus the age of their wives. It shows that ages among husband and wife have a high correlation (people tend to marry others around their same age).

http://cnx.org/content/m10949/latest/age_scatterplot.gif

Index Value Plot

An index is defined as a statistical indicator/number derived from a formula, which is used to characterize a set of data.

An index value plot is a type of visualization map that is plotted on a line graph.

http://www.mathworks.com/products/demos/shipping/garch/garchcopulaevtdemo_01_thumbnail.png

Accumulation Line Graph or Lorenz Curve

The Lorenz curve is used in economics and ecology to describe inequality in wealth or size. It is a graphical representation of the proportionality of a distribution (the cumulative percentage of the values).
A graph for showing the concentration of ownership of economic quantities such as wealth and income, it is formed by plotting the cumulative distribution of the amount of the variable concerned against the cumulative frequency distribution of the individuals possessing the amount.
The Lorenz curve above illustrates a representation of the cumulative distribution of income by population.
http://content.answers.com/main/content/img/oxford/Oxford_Geography/0198606737.lorenz-curve.1.jpg

Bilateral Graph

Bilateral graphs depict increases and decreases on either side of a zero line. They are used to display data of both positive and negative values. An example of a bilateral graph is shown below:

This bilateral graph is a depiction of fertility changes in Chile over the past 25 years. You can see from the graph that for most of the past 25 years there has been a decrease in fertility among Chileans, with the exception of a short period of increase in the late 80's early 90's.
http://clausvistesen.squarespace.com/storage/thumbnails/325258-1851195-thumbnail.jpg

Google Earth - Remote Sensing

The above image is a remote sensing image taken from MODIS active fire mapping program. The website for this is http://activefiremaps.fs.edu.us. It shows the number of active fires reported in the contintental US within the last 24 hours and is updated hourly.

Nominal area Choropleth Map

Nominal Area Choropleth maps are used to display nominal data over a specified region. Nominal data is defined as categorical data where the order of the categories is arbitrary, such as race, ethnicity, political party, hair color, etc...

Above we see nominal data (European nations) mapped to colors. Notice that the colors aren't in an organized scale in any sense. There are no obvious color ramps to imply order. We simply map nomimal values onto discrete colors.

http://web.cs.wpi.edu/~matt/courses/cs563/talks/nominal_data/geopolitical.gif

Unstandardized choropleth Maps

Unstandardized Choropleth Maps utilize data sets of raw numbers. The data displayed is not averaged but is represented as a total value.The above unstandardized Choropleth map dispays the number of water withdrawals by state across the US.
http://pubs.usgs.gov/fs/2005/3051/images/2000choropleth.gif

Standardized Choropleth maps

The data/information portrayed in standardized choropleth maps is "standardized" or "normalized", which allows for comparison of distribution among different areas.

The standardized choropleth map shows population density according to the states' areas in square miles.

http://upload.wikimedia.org/wikipedia/commons/thumb/7/78/USA_states_population_density_map.PNG/800px-USA_states_population_density_map.PNG

Univariate Choropleth Maps

Univariate Choropleth maps use basic choropleth mapping techniques to illustrate the distribution of one single variable through shades of color or patterns. The above map shows the distribution of average/median household income for states across the US. Each range of income is represented by a different color, and each state is colored according to where they fall in these ranges.

http://www.ats.ucla.edu/stat/sas/code/gmap.gif

Bivariate Choropleth maps

A bivariate choropleth map displays two variables on a single map by combining two different sets of graphic symbols or colors. It is a variation of simple choropleth maps that portrays two separate phenomena simultaneously while accurately and graphically illustrating the relationship between the two distributed variables. Bivariate Choropleth maps have the potential to reveal relationships between variables more effectively than side-by-side comparisons of the corresponding univariate maps.

The above Bivariate Choropleth map shows the relationship between crime rates and election results (votes for Kerry or Bush) in 2003.
http://www.geog.ucsb.edu/~jeff/gis/choropleth_maps_files/election04_vs_crime03b.jpg

Unclassed Choropleth Maps

In a conventional Unclassed Choropleth map, a continous ramp of shading or color intensity is used to illustrate a scale of data. The lowest and highest color intensities are assigned to the lowest and highest values respectively. A distinctive feature of unclassed choropleth maps is that each unique value has a unique shading of color. As you can see above, the scale for an unclassed choropleth map is a continuous grading of color, with each color representing a specific value.

http://www.princeton.edu/~rvdb/JAVA/election2004/purple_america_2004_small.gif

Classed Choropleth Maps

Choropleth maps portray areal data using areal divisions which are often boundaries defined by units such as counties or states. A Classed Choropleth Map shows data combined into a smaller number of groups which is then portrayed in intervals. The choice of the number of groups affects the resulting map greating. Some formal classsification techniques include equal step classification, classifying by quantiles, natural break classing, and minimum variance classification.

The above choropleth map is classified using equal steps classification. The total data range is first divided into categories chosen by the cartographer. A drawback to this technique is that there may be empty categories or categories with many members, as is the case here, since only one state falls into the highest category while many states fall into the second to lowest category.

http://www.ilstu.edu/~jrcarter/Geo204/Choro/map-AmFact-4eqint-orange-80pct.jpg

Range Graded Proportional Circle Map

In reference to Range Graded Proportional Circle Maps, the data is divided into groups and the cartographer chooses circle sizes for adjacent classes so that the map reader can easily distinguish between circle sizes, and therefore, categories. So, each circle size represents a specific range of data on the determined scale. An example of this type of map is shown below:

In the map above, the cartographer chose a series of different sized cirlces to represent specific amounts of data.

http://www.neiu.edu/~jrthomas/377/circle.jpg

DLG

Above you will see an example of a USGS hydrographic DLG of the Tsala Apopka Basin located in Citrus County, Florida.

DLG stands for Digital Line Graph. DLGs contain a wide variety of information, including but not limited to: topography, hydrography, boundaries, roads, utility lines, and vegetative surface cover. Digital Line Graphs (DLGs) are digital vector representations of cartographic information derived from USGS maps and related sources. Data about map features are stored as lines (arcs), points, and polygons (areas).

http://www.dooris-assoc.com/tsala1.jpg

Continuously Variable Proportional Circle Map

A proportional circle map is one in which point data is mapped with a circle instead of a dot. The size of the circle is directly related to the measured variable and NOT necessarily to the area over which it is measured. Specifically, with regards to a Continuously Variable Proportional Circle Map, the size of the circle used corresponds to a specific level of the measured variable in questions. There is no limit on the number or sizes of circles used because they are continuously graded along with the variable. So, as the size of the measured variable increases, the size of the circle will increase in direct proportion to the variable.

the continuously proportional circle map above is illustrating channel width through the use of proportional circles. The size of the circle is directly proportional to the width of the channel.

http://pubs.usgs.gov/fs/fs-004-03/images/fig5lg.gif

DOQQ

A Digital Orthographic Quarter-Quad, DOQQ, is a digitized image of an aerial photograph, corrected for displacements caused by camera angle and relief. The result is a spatially accurate image with planimetric features appearing in their true geographic positions. Distortion corrections are made through georectification (features on the map are linked to their real world positons through a coordianate system, datum, and projection) and orthrectification (distortion is removed so that the photo can be used as a flat map; ground features are displayed in their true positions, allowing for more accurate measurement of distance, areas, angles, and positions). Orthophotos combine the image characteristics of a photograph with the geometric qualities of a map.

The above DOQQ is of Brandywine, British Columbia.

http://www.wr.udel.edu/cb/b17doqqqpuzzle.jpg

DEM

DEM, Digital Elevation Model, is a digital file consisting of terrain elevations for ground positions at regularly spaced horizontal intervals. It is in raster format, so the cartographic dats is recorded, stored and processed in a cell or pixel. DEM's are georeferenced, meaning their features are tied into a coordinate system, datum, and map projection and reference specific locations (i.e. latitude & longitude) in space.

DEMs are commonly built using remote sensing techniques, however, they may also be built from land surveying. DEMs are used often in GIS, geographic information systems, and are the most common basis for digitally-produced relief maps.

Above you will see a DEM for Honolulu, HI. Note the use of shading to illustrate increasing elevation. The lowest level of elevation starts out with the dark shades of green, gradually lightening through shades of yellow, brown and white to represent those areas of higher elevation.

http://home.san.rr.com/bwagner/honolulu.dem.jpg

DRG

A DRG, digital raster graphic, is a scanned and georectified image of the paper version of the U.S. Geological Survey topographic maps. These provide a way to view the US Geological surveys in digital format. Most DRG's are made by scanning published paper maps on high resolution scanners, such as is shown on the DRG above.

http://topomaps.usgs.gov/images/drg_splash.jpg

Isopleths

An isopleth is also known as a contour line. It is a feature of some charts and maps, connecting points which have an equal value of some variable at a given time and spatial area. The particular variables shown may include values such as pressure, temperature, wind speed, population, etc. They are used to assist in visualizing the general features of an area. Some common types of isopleths include: isotherms (points of equal temperature); isobars (points of equal pressure); isohyets (points of equal precipitation). Below, you will see an illustration of the construction of an isopleth map, beginning with various values and ending with lines and shadings connecting those points of equal value.

http://www.fao.org/DOCREP/003/T0446E/T044648.gif

Isoplaths

An isoplath map is a type of contour line map that uses lines to connect areas of equal acidity's. These contour lines are known as isoplaths, hence the term "isoplath map." An example of an isoplath map is shown below:

http://www.globalchange.umich.edu/globalchange1/current/lectures/kling/water_nitro/USAacid_rain2.gif

Isohyets

An isohyet or isohyetal line is a line joining points of equal precipitation on a map. A map with isohyets is called an isohyetal map. Below is an example of an isohyetal map of Hong Kong:


http://www.hko.gov.hk/publica/tc/tc2002/images/figure/figure332.gif

Isotachs

Isotachs are contour lines on a map indicating equal wind speeds. So, all points along an isotach would have equal wind speeds. Below is a map with isotach contour lines of wind speeds across north america.

http://wxmaps.org/pix/avnmr5.00hr.png

Isobars

A line drawn on a weather map connecting points of equal pressure is called an isobar. That means, that at every point along a given isobar, the values of pressure are the same. The isobars are generated from mean sea level pressure reports and the pressure values are given in millibars.

The above is a map of isobars indicating areas of equal pressure across parts of Europe.
http://www.windfinder.com/grafiken/isobars/isobars_central_europe_1.gif

LIDAR

LIDAR stands for "Light Detection And Ranging". With LIDAR you can: measure distance; measure speed; measure rotation; and measure chemical composition and concentration. Light Detection and Ranging (LIDAR) is a remote sensing system used to collect topographic data.

This technology is used by the National Oceanic and Atmospheric Administration (NOAA) and NASA scientists to document topographic changes along shorelines, as illustrated in the LIDAR image below of Hilton Head, South Carolina:

In remote sensing, false color images are common. They serve as a means for visualizing data. The term "false color" refers to the fact that these images are not photographs. Rather, they are digital images in which each image pixel represents a data point that is colored according to its value. So, in LIDAR elevation maps, each pixel represents a certain elevation and is colored on the map accordingly to the color that corresponds to that particular elevation.
http://www.csc.noaa.gov/products/sccoasts/html/images/lhilt.gif

Doppler Radar

Doppler radar is a radar using the doppler effect of the returned echoes from targets to measure their radial velocity. It is a radar that produces a velocity measurement as one of its outputs.

Doppler radars are used in air defense, air traffic control, sounding satellites, police speed guns, and radiology.

The above is a doppler radar image taken at Buckland Park, Australia, indicating direction of winds (shown with arrows) and velocity of wind speeds (indicated by colors).

Recent weather radars process velocities of precipitations by Pulse-Doppler radar technique, on top of their intensities. Above is a pulse-doppler radar map of Hurricane Ivan, which struck the gulf coast on September 16, 2004.

http://mirror.bom.gov.au/weather/radar/about/images/doppler.gif

http://media.mgbg.com/wkrg/photos/weather/Ivan4amDoppler.JPG

Black & White Aerial Photo

1960 Black & White aerial photo of Delaware, Colorado.


2000 Black & white aerial photo of Delaware, Colorado.

Aerial photography is the taking of photographs of the ground from an elevated position. The term usually refers to images in which the camera is not supported by a ground-based structure.
Black and White Aerials can show the evolution of site conditions over time, as illustrated through the two aerial photos shown above.

Infrared Aerial Photo

Infrared Aerial Photography is a powerful tool that can be used to document changes to the environment, the health of forests, wetlands, bays and oceans, as well as many other applications.

Red tones in color infrared aerial photographs are almost always associated with live vegetation and the tone of red can be a guide to the density and health of the vegetation and how vigorously it is growing. Dead vegetation will tend to appear as various shades of tan or green. Thus infrared imagery is particularly useful for crop, forest, wetland, vineyard and other agricultural analayses.

Color infrared aerial photography is also useful for analyzing water depth and sediment content. Clear, clean water will appear very dark, close to a black tone. As sediment content increases the shades shift to blue color tones. Color tones of very shallow water may reflect predominantly the color tones of the soil beneath this water. Color infrared aerial photography is therefore uniquely useful for analyzing sediment flows.

In the infrared aerial photo above, which depicts the mouth of the Parker River in Massachusetts, you can see that the water appears to be clean and clear, since it takes on such a dark, blackish tone. Also, it is evident from the photograph that there is a great deal of vegetation at the mouth of this river, with the more dense areas of vegetation appearing as bright red.

http://ecosystems.mbl.edu/pie/data/MAP/irparker.jpg

Cartographic Animations

Cartographic Animations are compilations of 2D and 3D imagery used to visualize the dynamic aspects of atmospheric phenomena.

Cartographic animations can be used to depict such phenomena as the growth of a city, traffic accidents, population growth in urban regions and three-dimensional cartographic objects. The animation of maps has been predominantly associated with the representation of change over time.

http://uwacadweb.uwyo.edu/JSHINKER/animations/global/gifs/storagechg_web.gif

Statistical Maps

Statistical maps are used to display the distribution of some variable over a specified geographic area, usually defined by political boundaries. An example of a statistical map would be such as the one below, illustrating the distribution of the Internet, or the "connectivity of countries", across the globe.



The basis for statistical mapping is that any kind of data that can be expressed numerically/graphically and varies in quantity from place to place can be mapped.
http://personalpages.manchester.ac.uk/staff/m.dodge/cybergeography/atlas/landweber_version_16.gif

Cartograms

A Cartogram varies the size of geographic areas based on the data values associated with each area. Cartograms scale geographic areas to things such as population, GNP, electoral votes, etc...

The above map is a population cartogram of the world. As you can see, Asia is substantially "bloated" in comparision to the rest of the world's population.

http://www.ribbonfarm.com/wp-content/uploads/2007/07/population800x400.png

Flow Maps

Flow maps have been used for centuries to show the movement of objects or people from one location to another. They illustrate the flow of people in and out of countries (migration), import and export of goods and raw materials, as well as the flow of wealth across nations.

One example of the use of flow maps would be the illustration of the slave trade, and the movement of slaves from Europe to Africa to the Americas and Carribean, as shown below:

http://exploringafrica.matrix.msu.edu/images/slave_routes.jpg

Isoline map

Isoline maps are maps that use continuous lines to join points of the same value, i.e. equal altitudes (contour lines); equal temperatures (isotherms), etc...

The above Isoline map uses isothermic lines to divide up the continent of Australia into areas of equal tempatures during a typical month of January. So the two areas encompassed by cirlces/lines indicating 95 degrees means that entire area averages 95 degrees during the month of January.
http://mapmaker.rutgers.edu/355/interpolating-70-deg-contou.gif

Proportional Circle Map

Proportional circles map are statistical maps that use a series of circles in increasing/decreasing size to illustrate proportional quantititative measurements. The size of the circle associated with each area of the map is proportional to the variable being described on the map. For instance, the above map is a map of Europe with circles of variable sizes assoicated with each country. These circle proportionately represent the amount of internest users within each country. As you can see, Denmark (one of the smaller nations in Europe) has roughly the same amount of internet users as Norway or Sweden (countries several times bigger than Denmark).
http://www.geog.ucsb.edu/~jeff/gis/proportional_symbols_files/map2.jpg

Choropleth Map

Choropleth maps portray quantitative data as colors showing the density, percent, average value, or quantity of a phenomenon within the boundary of a certain geographic area. Sequential colors (color gradients) indicate increasing positive/negative data values.


A Choropleth map is a type of thematic map in which areas are shaded in proportion to the measurement of the variable being displayed on the map. Some examples include population density or political affiliation. It provides an easy way to visualize how a measurement varies across a geographic area. It also shows the level of variable within a region.
The above choropleth map shows areas of increasing harvest amounts if hay. The darker colors indicate areas of larger hay harvesting.
http://www.nass.usda.gov/research/atlas02/Crops/Hay%20and%20Forage%20Crops%20Harvested/Hay%20-%20All%20Hay%20Including%20Alfalfa,%20Other%20Tame,%20Small%20Grain,%20and%20Wild,%20Harvested%20Acres-choropleth%20map.gif

Dot Distribution map

Dot Distribution maps portray quantitative data as a dot, which represents a number of any particular phenomenon in question found within the boundary of a certain geographic area. The pattern of distributed dots reflects the general locations where the phenomenon most likely occurs. The pattern and number of dots within a geographic area reveal the density of the phenomenon in question. There are 2 types of dot-distribution maps: the first type is a traditional dot map showing the distribution of a phenomenon; and the second type is an increase/decrease dot map. This ype of dot-distribution map shows increasing (positive) and decreasing (negative) values of a phenomenon.

Dot distribution maps are especially helpful in showing population, portraying quantitative populations as dots. Say I wanted to illustrate population of the United States, with each dot representing a defined number of people. Below is a representation of what this would look like:

The white areas are the most populated areas of this nation, according to the 2000 census. each white dot represents a specific number of people, so those areas where the white dots are more concentrated are more densely populated.

http://www.census.gov/geo/www/mapGallery/images/2k_night.jpg

Propaganda map

Propaganda maps are political maps of collapse and possibilities. In other words, they illustrate the possible or desired outcomes of wars and conflicts. For example, the propaganda map below illustrates what Europe would have possibly have looked like, had Germany won WWII:


However, not all propaganda maps center around wars. Propaganda maps can be any map geared at influencing the behaviors and opinions of large numbers of people in order to acheive a desired outcome. Their main purpose is to influence or suade their audience in a certain direction. The map above was probably used to help suade other Germans into the war effort, depicting a future of great power and wealth for all Germans alike.
When thinking of propaganda maps, the game of "Risk" pops into my mind, of conquering the lands of your opponent and expanding your empire across the board.
http://strangemaps.files.wordpress.com/2006/09/sur-le-vif-germany-wins-001.jpg

Hypsometric map

Hypsometric maps represent the differing elevations of the earth's terrain through the use of shading and colors. Hypsometric colors are most common in small scale topographic maps and are applied as continuous gradients or intervals. Most often the shading gradient will begin with lighter/brighter colors depicting the lower levels of elevation, and as the elevation increases the shading becomes darker and darker. This is illustrated on the hysometric map of the Greek island of Boiotia. On the left hand portion of the map you can see the dark areas of shading which represents the highest points of elevation on the island, most likely a mountain.

http://www.uam.es/proyectosinv/sterea/beocia/images/figure_8_gis.jpg