by

Efraim Halfon

National Water Research Institute

Canada Centre for Inland Waters

Burlington, Ontario

Canada L7R 4A6

E-mail: info@butx.com

May 1995

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 twenty years ago, could be run on supercomputers ten years ago, on workstations three years ago, and now 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 (GIS). Through solid modelling, oxygen and temperature data collected on May 28, 1990 and August 8, 1990 in Hamilton Harbour, Lake Ontario, are mapped into voxels and visualized on a two dimensional screen. Various three dimensional representations of temperature and oxygen data including water masses with temperatures of less than 12 ^oC, 13 to 14 ^oC, 16 ^oC to 17 ^oC, and greater than 23 ^oC, and oxygen concentrations of less than 4 mg L^-1, 6 to 8 mg L^-1 and 10 to 12 mg L^-1 are displayed. The start of the oxygen depletion phenomenon on May 28 does not start at the bottom but starts at the surface at the southern shallow part of the lake and it evolves northward in an interesting pattern of chimneys. The calculation of the 3D representation allows the accurate computation of volumetric properties 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 lake has a volume of 253,947,500 m³, the water mass (May 28, 1990) at 12-13 ^oC had a complex three dimensional shape with a volume of 61,036,250 m³ and on August 8, 66% of the lake volume had oxygen levels over 4 mg L^-1 and suitable for fish growth, contrary to expectations. 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.

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 volumetric 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 a new visualization environment in scientific computing; for example Hibbard and Santek (1989) presented interesting uses in the earth sciences.

Kaufman (1991a) 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."

Halfon et al. (1993), Assel et al. (1994), Tartari et al. (1994) and Halfon and Howell (1995) recently presented two dimensional computer visualizations of limnological data, however a literature review has failed to identify volume visualization applications in limnology. Several reasons might have caused this delay: One is that since a lake is bounded by land from all sides, shoreline and bathymetry must be available in digitized form. Second, water quality data in lakes are usually collected at sparse locations while volume visualization algorithms need the data organized in a uniform grid with no missing values, thus extensive data preparation is necessary. Finally, as late as 1991 figures similar to those presented in this paper were created using a supercomputer (Shirley and Neeman, 1989; Mercurio, 1991) and displayed using workstations. Indeed, Kaufman (1991a) lists special-purpose hardware for volume visualization, whereas only three years later this entire paper is produced on a 486/50 personal computer.

Hamilton Harbour (also called Burlington Bay) is located at the western end of Lake Ontario, it has a triangular shape with maximum dimensions eight kilometres from east to west and five kilometres from north to south; the maximum depth in the middle of the bay is about 26 metres and an additional deep area is located at the east end (Fig. 1). A ten metre deep channel connects it to Lake Ontario. Hamilton Harbour has been widely studied in the past ten years (Charlton, pers. comm.) since it is one of the 42 areas of concern 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). Here, a framework is described to visualize and interpret 3D data. In this framework there are three steps: data collection, solid modelling 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).

Water quality data (water temperature, oxygen concentration, conductivity, pH, etc.) have been collected by Charlton (pers. comm.) every year since 1985 at 26 stations (the number of stations has slightly increased or decreased over the years). Figure 2 shows the station locations; eight cruises took place in 1990 and since samples were collected with an electronic probe data are available at all depths every few centimetres.

This area of computer graphics has arisen following the need for modelling objects as solids (Foley et al., 1991). A lake is also a volumetric object; associated with each point in the lake there is a water quality variable of interest. 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 represents some measurable properties (e.g., temperature, pH, conductivity, oxygen concentration, toxic contaminants concentrations, etc.) and the 3D volumetric data set resides in an integer grid of voxels called a cubic frame buffer.

The visualization process consists of several steps necessary to organize the data in the proper voxel format: A first step is to divide the area of interest into a grid; the grid chosen for Hamilton Harbour is 50 x 50 metres. The depth value in each grid unit was obtained by interpolation using the SAS contouring program and the bathymetric data, which were originally in sparse form, were organized into a fixed grid.

Following the grid pattern, each voxel was defined as a rectangular parallelepiped (which allows for resolution in the different axes) with dimensions 50 metres x 50 metres by 0.5 metres and the cube frame buffer has dimensions of 200 x 127 x 52 for a total of 1,320,800 voxels. Over 2,500 bathymetry data and 14,000 shoreline data are available from the Canadian Hydrographic Service. The choice of the number of voxels and their size is left to the user for several reasons: 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). However, the larger the number of voxels the larger is the computer memory requirement and the computing time.

The second step was to identify which voxels represent land (depth value of zero) and which water (grid depth value greater than zero). Out of the 1,320,880 voxels only 204,034 are water given the conical shape of the harbour. 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 metres and data collected along the depth axis have already a metric dimension associated with them (data collected at .1, .2, ..., etc. metres), station locations were converted from geographical to UTM coordinates [metres] before the interpolation was performed.

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 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 (1991) states 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 frame 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. For this application the Hamilton Harbour voxel values were stored in ASCII format and the data set was read into memory by the Spyglass® Slicer program (Spyglass, 1994). Slicer is a volume visualization software that can be used for scientific visualization; while the program focuses on the 3D primitives, it can also visualize the data using more traditional 2D primitives, such as surface rendering as slices and isosurfaces (three-dimensional equivalent of contour lines).

Surface rendering is defined as "an indirect technique used for visualizing volume primitives by first converting them into intermediate surface representation and then employing conventional computer graphics techniques to render them to the screen." (Kaufman, 1992). An isosurface (Levoy, 1988) is a surface where the data with the same values are interpolated together, for example a thermocline can be considered a three dimensional temperature isosurface. The surface can be rendered as a transparent or solid surface. The isosurface can also be coloured according to the values of the scalar field at the surface points (Mercurio, 1991).

Figure 3 shows temperature and oxygen concentration data collected on May 28 and August 8, 1990. Depth scale is exaggerated 200 times and the surrounding land is transparent. The bathymetry, a collection of over 2500 individual data points, shows a peculiar bottom with deep holes; in this case a two dimensional contour map may not portray the lake bathymetry as well as a three dimensional volume visualization view. Furthermore, the lake can be rotated around any of the three axes for a complete understanding of the bathymetry (Fig. 4). This feature 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." The lake has a maximum depth of 26 metres, but a number of dredged areas at the east ed of the lake can be noted. Some of these areas have depth of over 22 metres.

Water temperature on May 28, 1990 ranged from 11.2 to 18.9 ^oC and oxygen concentrations ranged between 3.8 and 15.5 mg L^-1; water temperature on August 8 ranged from 12 to 24 ^oC and oxygen concentrations ranged between 0 and 10.7 mg L^-1. Figures 3 to 7 show visualization of the temperature data collected on May 28, 1990 under different rendering options. Figure 4 shows temperature data in Hamilton Harbour from two viewpoints, from the north, and from the bottom and the north-west, respectively. The bay is heating from the west while temperature at depth is about 11 ^oC. 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 cutout view from the south: The northern part of the water surface is visible together with an east to west transect; this view augments the information not provided by Fig. 3 since water temperature inside the harbour is visible. Figure 6 shows a complementary cutout view: the water masses with temperature of less than 12 ^oC, 13 to 14 ^oC and 16 ^oC to 17 ^oC 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 metres: this water mass has a temperature of 13 to 14 ^oC. This information is not visible from the figures 3 to 6. Surface water is warm (about 18 ^oC) in the western part of the bay while at the eastern side some cold lake water is present.

Figure 7 shows water temperature contours in the form of slices at two different depths, surface and 15 metres. The circulation of the bay is complex and Hamblin (pers. comm.) is now developing a two dimensional mathematical model of this flow field: At the surface, currents are mostly from west to east following the prevailing winds with return flow at deeper levels. At the east end of the lake surface waters cool by mixing with Lake Ontario water that enters the bay from a channel and a downwelling can be observed (Fig. 7). Thus, just under the surface along the main east-west axis there is a current from west to east.

In August 1990 (Fig. 8) the 13 to 14 ^oC and 16 to 17 ^oC water masses are found at lower depths than in May (Fig. 6), at about 15 and 10 metres, respectively. The water mass at the east end of the bay, > 23 ^oC, has the same surface temperature as the western part of lake Ontario. In summer, conductivity values had decreased to a range of 460 to 670 and two water masses could be distinguished, one at the surface with conductivity 582 to 600 and one at the bottom of 503 to 514. Thus, from May 28 to August 8, some Lake Ontario water entered Hamilton Harbour, mixed with the harbour water and settled at the bottom.

Figures 9 and 10 show oxygen concentrations on May 28 and August 8, 1990, respectively, in a cutout similar to Fig. 6; the water masses with oxygen levels less than 4 mg L^-1, 6 to 8 mg L^-1 and 10 to 12 mg L^-1 are identified. Interestingly the water mass of 6 to 8 mg L^-1 has the same chimney pattern observed for the water temperature of 8 ^oC. On May 28, oxygen is abundant everywhere while on August 8 the oxygen concentration pattern (Fig. 9) shows anoxic, < 4 mg L^-1, conditions below ten metres in some areas.

The 3D representation allows computation of several volumetric properties: 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 1250 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 (Table 1) and its heat content. On May 28, the median volumetric temperature is 13 ^oC while on August 8, the median temperature is about 20 ^oC. The volumetric frequency distribution of temperatures is also very different on these two dates (Table 1). On August 8, 1990 (Fig. 9) the 13 to 14 ^oC and 16 to 17 ^oC water masses are found at lower depths than on May 28 (Fig. 6), at about 15 and 10 metres, respectively. The water mass at the east end of the bay, > 23 ^oC, has the same surface temperature as the western part of Lake Ontario. In summer conductivity values had decreased to a range of 460 to 670 and two water masses could be distinguished, one at the surface with conductivity 582 to 600 and one at the bottom of 503 to 514. Thus, from May 28 to August 8, some Lake Ontario water entered Hamilton Harbour, mixed with the harbour water and settled at the bottom.

A similar calculation can also be performed for oxygen (Table 2) and we can note the different frequency distributions in May and in August; this calculation is quite simple since each voxel has water quality values associated with it and these values can be summed or elaborated numerically as needs arise. About 34% of the lake had oxygen levels below 4 mg L^-1 on August 8, and conversely, 66% of the harbour had waters suitable for fish growth. On May 28, oxygen depletion does not start at the bottom, as it could be expected, but it starts at the surface at the southern shallow part of the lake and it evolves northward in the form of chimneys (Fig. 11).

Visualization in the physical and natural sciences is distinguished by the need to deal with data sets that are volumetric, randomly spaced, time varying and multi-variant. With this methodology limnologists can access, analyze, and visualize water quality data collected in three dimensions (geographical co-ordinates and depth). Manley and Tallet (1990) 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 process of collating the data also produces information since the properties associated with each voxel are suitable for volumetric analysis. With the development of fast personal computers and properly designed software, it is possible to visualize limnological data on a personal computer quickly (on average 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 proper data set.

Charlton (pers. comm.) has collected water quality data in Hamilton Harbour since 1985: After nine 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. The Hamilton Harbour Research project will have archived over a gigabyte of heterogeneous image data by the end of this year and the visualization tool permits a clear understanding of these data at a glance. The volumetric patterns of increasing temperature and decreasing oxygen content can be easily followed and understood. The relations between observed patterns and the complex circulations are also made evident through this approach.

Visualization showed three dimensional patterns not visible otherwise. Temperature data, for example, show the water masses present in the lake and their movement to the bay. The process of oxygen depletion can be followed in the three dimensional space and 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. All figures presented in this paper are available for distribution on the anonymous FTP site, ftp.cciw.ca (\incoming\halfon).

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 May 28, and August 8, 1990. Each voxel has a volume of 1250 m³.

─────────────────────────────────────────────────────────────────

May 28, 1990

Temperature No. of Volume of % of lake Heat Content

Range ^oC Voxels Voxels [m³] volume [J]

11-12 51228 6.40 10⁷ 25.22 2.08 10¹⁵

12-13 48829 6.10 10⁷ 24.03 3.19 10¹⁵

13-14 39688 4.96 10⁷ 19.54 2.80 10¹⁵

14-15 29608 3.70 10⁷ 14.57 2.24 10¹⁵

15-16 14590 1.82 10⁷ 7.18 1.18 10¹⁵

16-17 12942 1.62 10⁷ 6.37 1.12 10¹⁵

17-18 5775 7.22 10⁶ 2.84 5.28 10¹⁴

18-19 497 6.21 10⁵ 0.24 4.80 10¹³

1.42 10¹⁶

─────────────────────────────────────────────────────────────────

August 8, 1990

Temperature No. of Volume of % of lake Heat Content

Range Voxels Voxels [m³] volume [J]

12-13 10043 1.26 10⁷ 4.94 6.56 10¹⁴

13-14 22203 2.78 10⁷ 10.93 1.57 10¹⁵

14-15 15410 1.93 10⁷ 7.58 1.17 10¹⁵

15-16 11474 1.43 10⁷ 5.65 9.30 10¹⁴

16-17 11711 1.46 10⁷ 5.76 1.01 10¹⁵

17-18 9279 1.16 10⁷ 4.57 8.48 10¹⁴

18-19 6690 8.36 10⁶ 3.29 6.47 10¹⁴

19-20 8083 1.01 10⁷ 3.98 8.23 10¹⁴

20-21 8511 1.06 10⁷ 4.19 9.11 10¹⁴

21-22 13119 1.64 10⁷ 6.46 1.47 10¹⁵

22-23 50167 6.27 10⁷ 24.69 5.89 10¹⁵

23-24 31019 3.88 10⁷ 15.27 3.80 10¹⁵

24-25 5451 6.81 10⁶ 2.68 6.97 10¹⁴

2.04 10¹⁶

─────────────────────────────────────────────────────────────────

Table 2: Oxygen content of Hamilton Harbour on May 28, and August 8, 1990. Each voxel has a volume of 1250 m³.

─────────────────────────────────────────────────────────────────

May 28, 1990

Average No. of % of lake Oxygen

Oxygen Voxels volume [g]

3.5 61 0.03 2.66 10⁵

4.5 790 0.39 4.44 10⁶

5.5 1033 0.51 7.10 10⁶

6.5 4777 2.35 3.88 10⁷

7.5 19725 9.71 1.85 10⁸

8.5 59575 29.32 6.33 10⁸

9.5 28157 13.86 3.34 10⁸

10.5 15949 7.85 2.09 10⁸

11.5 12440 6.12 1.79 10⁸

12.5 11635 5.73 1.82 10⁸

13.5 12076 5.94 2.04 10⁸

14.5 16607 8.17 3.01 10⁸

15.5 20334 10.01 3.94 10⁸

Total 2.67 10⁹ g O₂

─────────────────────────────────────────────────────────────────

August 8, 1990

Average No. of % of lake Oxygen

Oxygen Voxels volume [g]

0.5 12927 6.36 8.08 10⁶

1.5 25958 12.78 4.87 10⁷

2.5 19451 9.57 6.08 10⁷

3.5 11347 5.59 4.96 10⁷

4.5 8873 4.37 4.99 10⁷

5.5 9043 4.45 6.22 10⁷

6.5 13772 6.78 1.12 10⁸

7.5 16800 8.27 1.58 10⁸

8.5 35527 17.49 3.77 10⁸

9.5 46332 22.81 5.50 10⁸

10.5 3127 1.54 4.10 10⁷

Total 1.52 10⁹ g O₂

Visualization in the physical and natural sciences is distinguished by the need to deal with data sets that are volumetric, time varying and multi-variant. The goal of this project is implementation of a system whereby researchers can access, analyze, and visualize water quality data collected in three dimensions (geographical co-ordinates and depth). Another objective of this research is to develop software that not only enables but encourages ecologists to more fully utilize time-varying, multi-dimensional data from Hamilton Harbour and other areas of concern. A literature review has failed to identify volume visualization applications in limnology, thus this effort of combining visualization algorithms and research in lakes might be the first to be published.

The Hamilton Harbour Research project will have archived over a gigabyte of heterogeneous image data by the end of this year. Other RAP sites are similarly amassing large, complicated data sets. Ecologists want to transform this raw data into useful information to provide new insight into long-term ecological phenomena. Unfortunately, the procedures, software tools, and user friendly interfaces necessary to facilitate access to these data sets are currently lacking which precludes analysis and subsequent visualization by ecologists. This project investigates approaches to visualization of sampled volumetric data collected in Hamilton Harbour, Lake Ontario. An aspect of this research is to carefully compare different approaches to certain aspects of visualization, particularly, the interpolation of 3D data, the mapping from numeric data to visual parameters such as colour and transparency, and methods of efficient volume traversal.