The inner structures of lakes can be revealed using volume visualization algorithms since lakes are three-dimensional objects that are explored by taking samples at various stations and at different depths. These algorithms did not exist 20 years ago, they could only be run on supercomputers 10 years ago, on workstations 3 years ago, and now they can be run on personal computers. Using computer graphics it is now possible to combine data, their three-dimensional location, and lake topography to create images of water quality patterns which supersede conventional surface, two-dimensional, graphics. Through solid modeling, temperature data collected on 28 May 1990 and 8 August 1990 in Hamilton Harbour, Lake Ontario, are mapped into voxels and projected onto two-dimensional screens. Various three-dimensional representations of temperature data are displayed including water masses with temperatures of less than 12°C, 13 to I4°C. l6°C to 17°C, and greater than 23°C. The calculation of the 3D representations allows the computation of volumetric properties, e.g., masses, since each voxel has water quality values associated with it and these values can be summed or elaborated numerically as needs arise. For example the harbor has a volume of 254 x 106 m3, and the water mass on 28 May 1990 at 12-13°C had a complex three-dimensional shape with a volume of 61 x I06 m3. A third benefit of visualization is that the data can be viewed interactively from different viewpoints thus increasing the interaction between scientist and the data. These methods should also be able to be used in other limnological applications such as visualization of sediments, algal blooms, and other biological and chemical data.

INDEX WORDS: Lake Ontario, temperature, oxygen, 3D data visualization.

In traditional (pre 1970) computer graphics, polygons and lines (e.g., a wireframe) represented three-dimensional (3D) volumetric objects. Conversely, some 3D data sets, e.g., the 3D water quality patterns collected in a lake, might not consist of surfaces and edges at all. Greenleaf et al. (1970) were the first to introduce new methods of visualization to extract information from volume data: this process called volume visualization is defined by Kaufman (1992) as "a direct technique for visualizing volume primitives without any intermediate conversion of the volumetric data set to surface representation."

The first applications were in medical imaging and they are still dominant (e.g., Adams et al. 1990, Rhodes et al. 1987). McCormick et al. (1987) stated that volume visualization was emerging as anew visualization environment in scientific computing; for example Hibbard and Santek (1989) presented interesting uses in the earth sciences. Manley and Tallet (1990), who used both mathematical models as well as data to understand the system they were studying, noted that "the ability to visually manipulate and gain quantitative information from three-dimensional models provides more information to the researcher over a significantly shorter period of time that a myriad of cross-sections and planar maps." The development of volume visualization software for PCs has been rapid: As late as 1991 figures similar to those presented in this paper were created using a supercomputer (Shirley and Neeman 1989, Mercuric 1991) and displayed using workstations. Indeed, Kaufman (199l a) lists special-purpose hardware for volume visualization. Kaufman (199la) provided an insight into this technology stating that "the objective of volume visualization is to peer inside the volumetric objects to view that which is not ordinarily viewable and to probe into the voluminous and complex structures and their dynamics to comprehend that which is not ordinarily comprehensible."

Hamilton Harbour (also called Burlington Bay) is located at the western end of Lake Ontario. It has a triangular shape with maximum dimensions 8 kilometers from east to west and 5 kilometers from north to south. The maximum depth in the middle of the bay is about 26 meters and an additional deep area is located at the east end (Fig. 1). A 10-meter-deep channel connects it to Lake Ontario. Hamilton Harbour has been widely studied in the past 10 years (Charlton, pers. comm.) since it is one of the 42 Areas of Concern identified by the International Joint Commission within the Great Lakes and furthermore the International Council for Local Environmental Initiatives has designated the city of Hamilton as Canada's model city under the United Nations Agenda 21 program (ICLEI 1990).

Halfon et al. (1993), Assel et al. (1994), Tartar! et al. (1994, 1995), and Halfon and Howell (1995) recently presented two-dimensional computer visualizations of limnological data. Here, a framework is described to visualize and interpret 3D data. In this framework there are three steps: data collection, solid modeling or transformation of the data in a specific volumetric format, and finally volume rendering or the visualization process. For general applications consult Kaufman (1991b), Foley et al. (1991), and Bergeron and Kaufman (1994).

Over 2,500 bathymetry data and 14,000 shoreline data are available from the Canadian Hydrographic Service. Water quality data (water temperature, oxygen concentration, conductivity, pH, etc.) have been collected by Charlton (pers. comm.) every year since 1985 at 26 stations every 2 or 3 weeks (the number of stations has slightly increased or de-creased over the years). An electronic probe has been used to collect data from the surface to the bottom every few centimeters. Figure 2 shows the station locations; eleven cruises took place in 1990. The visualization process consists of several steps necessary to organize the data in the proper format. A first step is to divide the area of interest into a uniform grid; the grid chosen for Hamilton Harbour is 50 x 50 meters. The depth value in each grid unit was obtained by interpolation using the SAS con-touring program and the bathymetric data, which were originally in sparse form, were also organized into a fixed grid. Thus, a major requirement is that shoreline and bathymetry must be available in digitized form.

Interpolation of the water quality data from scattered stations to a uniform grid was performed using water quality parameter data collected at the nearest three stations. Weight factors were inversely proportional to the square of the distance from the three closest stations. Interpolation was performed in two dimensions, one layer at the time. Interpolation in the vertical axis was performed using the IMSL (1987) subroutine SCAKM which uses a spline function to interpolate the data. A spline interpolation could not be used in the horizontal plane since the IMSL subroutine SURFER could not be constrained to have the interpolated data stay within the observed range. The interpolation problem, that is fitting the data collected at arbitrarily located positions to a uniform grid, is complex. While this problem has not been fully solved, Foley et al. (1993) have reviewed past work and proposed solutions.

The rationale of choosing a 50 m by 50 m grid was a compromise between geographical considerations and rendering speed on a PC. As the number of cells increases, grid size diminishes, the ambiguity between land and water voxels decreases, but it does not disappear, unless the lake is a perfect cube (unlikely). The shoreline in the southern part of the harbor is completely artificial following the needs of the steel companies on its shores. To show all the piers a resolution of ten of meters is necessary but no new knowledge is gained by a very fine grid since most of the grid data are interpolated (In medical applications a very fine grid is necessary since a surgeon needs real data on all grid points to minimize risk during an operation). The compromise reached for Hamilton Harbour was a grid of 50 m x 50 m by 0.5 meters. The depth of 0.5 meters was chosen to preserve the vertical information collected with the probe.

Most volume visualization packages have been developed for workstations. These include SGI Explorer, which comes with all Silicon Graphics workstations; AVS, PV-Wave, Khoros, Data Explorer from IBM; Dynamic Graphics, and several public domain tools packages including VolVis, from SUNY Suny Brook; SciAn from Florida State University; and others from NCSA at the University of Illinois at Urbana-Champaign and SDSC (San Diego Super Computer Center). The drawback in using these packages includes the cost of the hardware (about $10,000) and software that costs $5,000 to $10,000 for each commercial program. For this application, I used the volume visualization software Spyglass® Sheer (Spyglass 1994) on a 486/50 personal computer. While the program focuses on 3D applications, it can also visualize the data using more traditional 2D methods, such as surface rendering as slices and isosurfaces (three-dimensional equivalent of contour lines). One of the advantages of this package is that ASCII data can be easily entered into the program. Once this is done the creation of complex 3D views is per-formed in less than a minute at a 640 x 480 resolution with 256 colors. Conversely, workstations can produce much better graphics with very high resolution and millions of colors, but rendering time for each picture will range from 15 to 45 minutes.

This area of computer graphics has developed following the need for modeling objects as solids (Foley et al. 1991). A lake is also a volumetric object; associated with each point in the lake there is water quality information. The "point," or cell, in the lake is of course related to the resolution used in the computer representation and the cells are a collection of adjoining nonintersecting solids. When the cells are equal and arranged in a fixed, regular grid, they are called voxels (volume elements), analogous to pixels. Each voxel is a quantum unit of volume and has a numeric value (or values) associated with it that represent measurable properties (e.g., temperature, pH, conductivity, oxygen concentration, toxic contaminants concentrations, etc.). The 3D volumetric data set resides in an integer grid of voxels called a cubic frame buffer.

Following the grid pattern, each voxel is defined as a rectangular parallelepiped (which allows for different resolution in the different axes) with dimensions 50 meters x 50 meters by 0.5 meters and the cube frame buffer has dimensions of 200 x 127 x 52 for a total of 1,320,800 voxels.

The second step is the identification of which voxels represent land (depth value of zero) and which water (grid depth value greater than zero). Out of the 1,320,800 voxels only 204,034 are water, given the conical shape of the harbor. A 3D array was created where each land voxel was assigned a value of zero and each water voxel a value of one. A similar procedure was followed with the water quality data. Since voxels have dimensions of cubic meters and data collected along the depth axis have already a metric dimension associated with them (data collected at .1, .2, .... etc. meters), station locations were converted from geographical to UTM coordinates [meters] before the interpolation was performed.

The third step was to join the voxels with their water quality values through Boolean algebra, this process has been defined by Manley and Tallet (1990) as "clipping."

Kaufman (199l a) stated that "to visualize the volume data set, the voxels can be projected into 2D pixel space and stored as a raster image frame in a buffer. This process, which is termed volume rendering (Drebin et al. 1988, Frenkel 1989, Levoy 1988, Upson and Keeler 1988), involves both the viewing and the shading of the volume image." The definition of Foley et al. (1991) is that "volume rendering is the process of displaying scalar fields," where a scalar field is a collection of all the numbers associated with each point in a volume. In summary "volume rendering is a direct display of volume primitives without any intermediate conversion of volume data to surface representation." (Kaufman 1991a). There is no a priori assumption that "the data consist of tangible surfaces that can be extracted and visualized." Specialized algorithms have been developed to render clouds, humans, and living objects (Blinn 1982, Herman and Udupa 1983). The application of volume rendering techniques to limnology is therefore not complex, but it requires the data preparation explained above.

Kaufman's (1991b) book can be consulted for a comprehensive review to create 2D projections from the 3D volumetric data, as well as volume rendering and shading. The fundamental algorithms fall into two categories, direct volume rendering (DVR) algorithms and surface-fitting (SF) algorithms. DVR methods are most appropriate for creating images from data sets containing amorphous features like clouds, fluids, and gases (Elvins 1992). Several algorithms have been invented to generate volume visualizations. They include color connecting (SF, Keppel 1975), marching cubes (Wyvill et al. 1986) and ray-casting (DVR, Tuy and Tuy 1984). Ray-casting is most often used to produce high quality images while for most other projects marching cubes and dividing cubes (Cline et al. 1988) are used.

The choice of colors is also complex. The program that I use in this application. Spyglass® Slicer (Spyglass 1994), automatically scales the data values from the original range, for example 3 to 25 degrees, to an arbitrary range of 0 to 255. Each of these numbers are then assigned a color. Slicer has a color control menu that allows the user to test a variety of color combinations in real time, before a final palette is chosen. For example for the water temperature, the blue color was associated with cold water and the red color with warm water. However, a number of intermediate colors, greens and yellows, had to be added to visualize different water temperatures in May, when the lake is fairly cool and the differences in the temperatures in the water masses are small but significant and in summer when a large temperature range exists between the surface and the bottom.

The figures presented in this paper are examples of applications of three-dimensional visualization techniques, and do not include a full analysis of water quality data in Hamilton Harbour since these data have not yet been published.

Figure 3 shows temperature data collected on 28 May and 8 August 1990. Depth scale is exaggerated 200 times and the surrounding land is transparent. Figure 3 can be used to analyze both the temperature data as well as the bathymetry of the harbor.

The bathymetry shows a peculiar bottom with deep holes, the lake has a maximum depth of 26 meters, but a number of dredged areas at the east end of the lake can be noted. Some of these areas have depths of over 22 meters. In this case a two-dimensional contour map may not portray the lake bathymetry as well as a three-dimensional view. Furthermore, the lake can be rotated around any of the three axes for a more complete visualization of the bathymetry:

Figure 4 shows temperature data (Murray Charlton, personal communication) in Hamilton Harbour from two viewpoints, from the north (a), and from the bottom and the northwest(b), respectively.

The ability to be able to change the viewpoint is very important since, as Manley and Tallet (1990) have stated, "no single view can reveal the spatial relationships within the volume and therefore we can gain a more thorough understanding of the represented physical environment."

Since this paper deals with the technology of viewing limnological data with volume visualization algorithms, only temperature data from two cruises are presented. Water temperature on 28 May 1990 ranged from 11.2 to 18.9°C and on 8 August ranged from 12 to 24°C. Figures 3 and 4 show temperature data collected on 28 May 1990. The bay is heating from the west while temperature at depth is about 11°C. These views allow an understanding of the temperature field at the surface, along the shores, and at the bottom, but they do not allow a view of inner parts of the lake.

Figure 5 is a cut-out view of the data from the south: The northern part of the water surface is visible together with a vertical slice along an east to west transect to a depth of 26 meters. This view augments the information shown in Figures 3 and 4 since water temperatures inside the harbor are visible. Figure 6 shows a complementary cut-out view: the water masses with temperature of less than 12°C, 13 to 14°C, and 16°C to 17°C are visualized while all others are transparent. One interesting feature is a convective chimney extending from the water surface to a depth of about ten meters in the NE corner: This chimney might be related to upwellings and has a temperature of 13 to 14°C. This information is not visible in Figures 3 to 6. Surface water is warm (about 18°C) in the western part of the bay while some cold lake water is present at the eastern side.

In August 1990 (Fig. 7) the 13 to 14°C and 16 to 17°C water masses are found at lower depths than in May (Fig. 6), at about 15 and 10 meters, respectively. The water mass at the east end of the bay, > 23°C, has the same surface temperature as the western part of lake Ontario

Volumetric Properties

The organization of data in a format useful for visualization permits the computation of several volumetric properties. For example, even if the bathymetry is uneven, the total lake volume can be easily computed by multiplying 231,053 voxels by the volume of each voxel (50 m x 50 m x 0.5 m or 1,250 m3) for a total of 253,947,500 m3. Other properties, laborious to calculate through standard two-dimensional projections (since these water masses have complex three-dimensional shapes) are, for example, the water volume at a given temperature (Table1) and its heat content. On 28 May the median volumetric temperature is 13°C while on August 8, the median temperature is about 20°C. The volumetric frequency distribution of temperatures is also very different on these two dates (Table 1).

A volumetric frequency distribution calculation can also be performed for oxygen (Table 2) and we can note the different frequency distributions in May and in August. On 8 August about 34 of the lake had oxygen levels below 4 mg L~1- Conversely, 66 of the harbor had waters suitable for fish growth. The mass of oxygen present in August was about 57 of that present in May.

Visualization in the physical and natural sciences is distinguished by the need to deal with data sets that are 3D, randomly spaced, time varying, and multivariant. With this methodology limnologists can access, analyze, and visualize water quality data collected in three-dimensions (area and depth). The data that can be analyzed with this graphical technique are not limited to water quality variables. The process of collating the data for visualization also produces information since the properties associated with each voxel are suitable for volumetric analysis as done here for temperature and oxygen. Distribution of toxic contaminants, distribution of sediments in the water column and at the bottom, etc., can be easily visualized when the data are available. For example, sediment cores are a set of three-dimensional data that could be used to visualize processes taking place at the water-sediment interface and within the sediments. With the development of fast personal computers and properly designed software, it is possible to visualize limnological data on a personal computer quickly (about 30 seconds are needed to render each figure presented in this paper) once the data have been interpolated and saved in a format suitable for volume visualization. This time frame contrasts with the months needed to collect a valid data set.

Charlton (pers. comm.) has collected water quality data in Hamilton Harbour since 1985. After 9 years of sampling, the amount of data available for analysis is quite extensive, since data are collected seven or eight times a year at over twenty-five stations at over fifty depths per station. The Hamilton Harbour research project will have archived over a gigabyte of heterogeneous data by the end of this year, and the tool presented here permits a clear visualization of these data at a glance. The volumetric patterns of increasing temperature and decreasing oxygen content can be easily followed and understood and the masses involved easily calculated. The relations between observed patterns and complex circulations can also be made evident through this approach.

Visualization shows three-dimensional patterns not otherwise visible. The visualization of the temperature data, for example, shows the water masses present in the lake. The process of oxygen depletion can be followed in 3D space. The volume (through the number of voxels) with given water quality properties can be easily computed for further analysis. A benefit of visualization is also that the data can be viewed interactively from different perspectives and with different viewing options thus increasing the interaction between scientist and the data.

Murray Charlton provided his unpublished data collected in Hamilton Harbour. Jackie Dowell prepared the FORTRAN program to convert the data to the volume visualization format and create the appropriate masks. Robert Coker gave useful suggestions, helped with the editing and gave creative assistance in the rendering process. Spyglass Corporation provided a beta version of their program Slicer.

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TABLE 1. Heat content of Hamilton Harbour on 28 May and 8 August 1990. Each voxel has a volume of 1,250 m³ (Return to text)

(Return to text)

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