Visualization of Stratospheric Ozone Depletion and the Polar Vortex

Lloyd A. Treinish
`lloydt@watson.ibm.com`

IBM Thomas J. Watson Research Center
Yorktown Heights, NY

Introduction

In the earth and space sciences, it is very common to organize geographically located data as a rectilinear grid with horizontal extent over the entire surface of the earth (i.e., latitude and longitude). In two dimensions that implies a topological primitive that is a rectangle of various sizes. In three dimensions the cell is a parallelpiped, with the height corresponding to altitude or atmospheric pressure, for example. These rectilinear mesh structures are ill-suited for the study of phenomena that occur continuously over a nominally spherical surface (i.e., they tear the data). In addition, these grids may not be fully populated due to missing data (i.e., when observations could not be made). In such cases, the grids could be viewed as being irregular.

Independent of grid type, cartographic techniques are often introduced to suitably deform the data to compensate for the problems inherent in the original structure (i.e., the use of a rectilinear representation for a spherical surface). Traditionally, such a transformation is accomplished by defining a new cartesian grid in the cartographic projection coordinate system, and then interpolating from the original rectilinear grid to the new one prior to any other operation. Given the curvilinear nature of such transformations, non-linear interpolation techniques are typically required to make the transformation of acceptable quality. Figure 1 illustrates this operation schematically in which the data values at three points in the original rectilinear, regular grid are combined to define the value at a single point in transformed space (e.g., the values are weighted averaged, where the weight is a function of distance from their original points to that in transformed space). In addition to being computationally expensive, such interpolation makes it impossible to preserve the fidelity of the data prior to rendering, especially if regions of no data or other discontinuities are present. Such discontinuities would be smoothed out.

Figure 1. Data Transformation by Interpolation.

Alternatively, by warping the underlying mesh structure, the geometry itself is transformed without affecting the data. Figure 2 illustrates this operation schematically in which there is a one-to-one mapping of each point in the original and the transformed grid. At each node in the deformed grid there is a data value that corresponds to a specific node in the regular grid.

Figure 2. Grid Transformation by Coordinate Warping.

Thus, any realization (the application of one or more visualization strategies that generate renderable geometry from a collection of data) is independent of the choice of a specific cartographic coordinate system, the data or mesh themselves, or how the data are specified with respect to the underlying mesh (e.g., assigned at each node or to an entire cell at its center). In addition, interpolation is not required as the initial operation to be applied to the data to be visually correlated. Instead, interpolation can be isolated to be the last step in the visualization process, namely rendering (e.g., Gouraud-shaded surfaces).

The use of appropriately warped curvilinear grids can preserve the fidelity of the data prior to rendering. This does require an environment that supports direct realization and rendering of data on curvilinear grids as well as regular ones. This must be coupled with the ability to independently manipulate data and its underlying mesh structure or base geometry. In addition, the ability to simultaneously render disparate geometry (e.g., points, lines, surfaces and volumes of varying color and opacity) is very helpful in viewing the realization of multiple data sets.

Correlative visualization implies two tenets. First is the capability to look at multiple sets of data in exactly the same fashion (i.e., visual comparison within a common framework). That is, displaying different sets of data of disparate structure in an arbitrary geographic coordinate system independent of the data sets. Second is the capability to utilize a variety of visualization strategies within the chosen coordinate system, for examining a single set of parameters from one source or many parameters from multiple sources. Specific representation techniques illustrate different aspects of data. Hence, no single method is always suitable and not all techniques are useful for all data sets.

Therefore, methods that support the registration of multiple data sets in geographic coordinates, using similar cartographic warping of the respective data locations for the data sets in question shows promise as an alternative to meshing, interpolating or resampling the original grids of each data set to a common rectilinear grid in projected space for correlative visualization in the earth and space sciences. The former is used via the IBM Visualization Data Explorer developed by IBM Thomas J. Watson Research Center [Abram and Treinish, 1995]. This is in contrast to the latter approach used by the author via the NSSDC Graphics System, developed by NASA/Goddard Space Flight Center [Treinish, 1989] [Treinish and Goettsche, 1991].

Stratospheric Ozone Depletion and the Polar Vortex

The aforementioned approach for the analysis of multiple data sets via correlative visualization can be illustrated by an example scientific problem. There is a phenomenon that occurs in the earth's upper atmosphere (primarily the stratosphere) above Antarctica during the winter and early spring of every year known as the polar vortex [Schoeberl and Hartmann, 1991]. This effect is characterized by a cyclonic circulation pattern around the south pole. Many researchers believe that ozone-destroying chemicals are trapped in this vortex during the cold and dark of Antarctic winter. Once spring begins and the polar region emerges from the long night, it is theorized that these substances react photochemically with ozone to break the molecule apart and thus, aid in the creation of the so-called Antarctic ozone hole. Hence, in late winter, regions of ozone depletion around the pole begin to form. Within a few weeks the ozone hole is completely established. By late spring the vortex weakens, causing the ozone depletion region to fragment and eventually dissipate. The question of interest is, what are the characteristics of the south polar vortex that can be derived from diurnal observations of atmospheric dynamics and how do they relate to independent measurements of ozone? The study of the appropriate data sets for the southern hemisphere winter and spring (June through December) are relevant. The examination of a single year, 1987, is made because that year showed the greatest amount of ozone depletion until recent years [Krueger et al, 1992].

Total Column Ozone Data

Perhaps the most critical effort to study stratospheric ozone has been via observations made by the Total Ozone Mapping Spectrometer (TOMS) aboard NASA's Nimbus-7 spacecraft. Nimbus-7 is in a (polar) sun-synchronous orbit, which means that it can roughly provide global coverage of the earth for its suite of instruments once per day. Each portion of the earth was observed nominally under the same illumination conditions from day to day. Measurements made by Nimbus-7 TOMS show the daily global distribution of stratospheric ozone from late 1978 until early May 1993. It measured the total column density of stratospheric ozone by observing backscattered solar ultraviolet radiation in seven spectral bands. Approximately 200,000 such measurements were made each day, which covered the entire globe [Fleig et al, 1986].

TOMS required sunlight to operate. Hence, there are periods of missing data due to local polar winters (i.e., it is dark) in addition to the usual data dropout problems associated with spacecraft observations. These regions are visible as gaps in various realizations of the data. They are NOT the ozone hole. The data have been gridded in a regular lattice of 180 (1.0 degree in latitude) x 288 (1.25 degree in longitude) from the raw observations for daily global coverage with cells without data being flagged. The locations of missing cells are considered in all realizations. The total ozone measurements are in Dobson Units (DU), corresponding to a column density of 2.69 x 10^16 molecules of ozone cm-2.

Figures 3a and 3b show traditional two-dimensional visualizations of the ozone data on October 1, 1987, which is during the ozone depletion season. The rectangular presentation of the data is consistent with the provided mesh in that it is torn at the poles and at a nominal International Date Line. This cartographic representation of the earth is known as a cylindrical equidistant or plate carre projection. The ozone data are overlaid with a map of world coastlines and national boundaries. In Figure 3a the data are realized as iso-contour lines at 50 DU intervals, which indicate the spatial distribution of discrete thresholds within continuous data. In Figure 3b a pseudo-color spectrum is used, which is linearly mapped over a range (110 to 650 DU) valid for the year of study (i.e., to provide consistent comparisons between single days or for animation), and should provide a continuous representation of continuous data. Figure 3b also has a fiducial overlay (lines of latitude or parallels and longitude or meridians at 30-degree spacing) in white, which have been registered in this same rectilinear coordinate system. The grid cells where there are no data are visible as gaps in the pseudo-color realization. The area of low ozone is visible as a bluish band stretched across the bottom of the pseudo-colored rectangle.

Figure 3a. Contour-mapped global column ozone on October 1, 1987.

Figure 3b. Pseudo-color-mapped global column ozone on October 1, 1987.

Figure 4 shows the same representation as Figure 3b, but transformed by the Mollweide cartographic projection. In addition, iso-contours lines at every 20 DU have been overlaid to help in the interpretation of the pseudo-color image. The ozone density value for each line has been used to assign the same color to the line as the surrounding image, but at a lower level of brightness. The Mollweide and similar projections are used relatively often by earth scientists as a way of preserving area in a display of the entire globe compared to the cylindrical equidistant projection. Other projections may preserve shape or linear distance, for example, on selected portions of the globe [Pearson, 1990]. For the Mollweide projection, all meridians, which converge at the poles, are ellipses except for the central meridian, which is a straight line and considered (a) true (representation of a line on the earth's surface). For example, the 90 degrees meridians are circular arcs. The parallels are straight lines perpendicular to the central meridian. The equator is considered true. The Mollweide projection can be characterized by the following:

x = R sin(latitude)

y = longitude cos(latitude)

where [latitude, longitude] represents the location of each node on the earth's surface in the original mesh,
R is a scaling radius (e.g., 90 degrees) and
[x, y] represents the location of each node in the deformed, curvilinear (Mollweide) coordinate system with an assumed pole point of 90 degrees north latitude and 0 degrees east longitude.

Figure 4. Mollweide warped pseudo-color-mapped and contoured global column ozone on October 1, 1987.

To examine a continuous phenomenon with a central focus far from the equator and the Prime Meridian, such as the ozone hole, either a different pole point for the Mollweide projection must be used or in this case it would be appropriate to use a different map projection. Figure 5 illustrates the same data as in Figures 3 and 4 except a polar orthographic projection for both the southern and northern hemispheres is employed, which are shown in the left and right side of the Figure, respectively. For the orthographic projection, all meridians are straight lines radiating from the central pole. The parallels are concentric circles, which become compressed toward the equator. The orthographic projection can be characterized by the following:

x = R cos(latitude) cos(longitude)

y = R cos(latitude) sin(longitude)

where [latitude, longitude] represents the location of each node on the earth's surface in the original mesh,
R is a scaling radius (e.g., 90 degrees) and
[x, y] represents the location of each node in the deformed, curvilinear(orthographic) coordinate system with an assumed pole point of 90 degrees north latitude and 0 degrees east longitude and an assumed pole point of 90 degrees south latitude and 0 degrees east longitude for the northern and southern hemispheres, respectively.

Figure 5. Southern and northern hemisphere orthographic warped pseudo-color-mapped deformed surfaces of global column ozone on October 1, 1987.

In addition to the pseudo-color spectrum, this two-dimensional cartographic projection of the data is extended by redundant realization as a deformed surface (i.e., both height and color correspond to ozone density). The bluish contiguous area over Antarctica clearly depicts the depletion region, illustrating the advantage of choosing an appropriate cartographic coordinate system. The height mapping clearly dramatizes the concept of a depression in the ozone layer while the color enhances this perception as color enhances a topographic map. It provides a continuous representation consistent with the spatial structure of the data and in animation presents the dynamics in an easily discernable fashion.

It should be noted that the use of hue-based pseudo-color mapping for realization and rendering of data as images can create problems in interpretation due to how the human visual system responds to color [Rogowitz et al, 1992]. For example, discontinuities appear in the pseudo-color representation (e.g., Figure 3b) that are not in the data but are due to how humans perceive hue (i.e., discretely). However, such pseudo-color maps are virtually standard in many disciplines. The acceptance of alternate, perceptually correct pseudo-color maps (e.g., luminance-based, [Lefkowitz and Herman, 1992]) would be limited in these disciplines because of their unfamiliarity. Therefore, the introduction of redundant realization techniques such as surface deformation retains the familiar pseudo-color scale but helps to lessen its negative perceptual impact.

Below each translucent surface is a hemispherical map that has been registered in the same orthographic coordinate system as the ozone data. This map consists of a monochromatic topographic surface, which is deformed based upon height above or below sea level. The monochromatic scale is chosen to impart the appearance of a topographic map (e.g., the oceans are dark gray) for each hemisphere. This surface is created from a topographic data base on a rectilinear grid at 0.5 degrees resolution. The grid is warped by the same orthographic projection that was applied to the ozone data, although the data were originally in a different coordinate system at different resolution. Both the ozone and topographic surfaces are Gouraud-shaded. In addition, the topographic map is overlaid with the same coastline map in magenta with political boundaries corresponding to each hemisphere that was used in Figures 3a and 3b. The map geometry was transformed in a manner similar to that of the ozone and topographic data.

There is a seam in each of the orthographic surfaces corresponding to where east longitude is either -180 degrees or +180 degrees, nominally the International Date Line, which is an artifact of the warping of the original rectilinear data onto a continuous surface, welding the discontinuity in the provided form of the data. The use of coordinate warping does preserve this inherent discontinuity in the data, which would not be the case if traditional interpolation techniques were chosen. In general this seam will not smoothly connect the surface due to how TOMS gathers data. This scanning instrument examined each portion of the earth at a different time of day, but still covering the entire globe once per day. Hence, observations on each side of that line were taken approximately 24 hours apart and usually are not the same.

Figure 6 carries this cartographic theme to a three-dimensional continuous surface by performing a cartesian to spherical coordinates transformation. For the spherical projection, all meridians are great circles converging at the poles. The parallels are also great circles, which become compressed toward the poles. The spherical projection can be characterized by the following:

x = (h + r)cos(latitude)sin(longitude)

y = -(h + r)cos(latitudej)cos(longitude)

z = (h + r)sin(latitude)

where [latitude, longitude, r] represents the location of each node on the earth's surface as [latitude, longitude] at its radial distance, [r], from the earth's center in the original mesh,
h is the height above the (radial) surface of the earth, and
[x, y, z] represents the location of each node in the deformed, curvilinear (spherical) coordinate system.

The ozone is now triply redundantly mapped to height (now radial), color and opacity so that high ozone values are thick, far from the earth and reddish while low ozone values are thin, close to the earth and bluish. Replacing the map for annotation is a globe in the center of this ozone surface, which is created from the same topographic data used in Figure 5. The topography is warped onto a smooth, Gouraud-shaded opaque sphere (i.e., 259,200 polygons) and pseudo-colored to give the appearance of a globe by having all values around sea level and below appear light blue. The topography and ozone data are registered in a common spherical, earth-centered coordinate system. As with Figure 5, southern and northern hemispheric views are shown, which are shown in the left and right side of the Figure, respectively. Each spherical object gives the appearance of looking at a continuous phenomenon from two vantage points. The use of three redundant realization techniques results in patterns or textures, which are particularly effective in animation of time sequences for qualitatively identifying regions of spatial or temporal interest in the data. Such an approach shows promise for data browsing. On the other hand, the orthographic projection technique does not yield such an impression, although it does impart more of a quantitative "feel" to the visualization. Hence, this projection will be revisited in the subsequent discussions.

Figure 6. Southern and northern hemisphere views of radially deformed pseudo-color and opacity-mapped spherically warped surfaces of global column ozone on October 1, 1987.

Dynamics Data: Atmospheric Temperature and Winds

Global atmospheric dynamics data (e.g., temperature and wind velocity) are often derived from spacecraft, balloon and aircraft observations, which have been modelled and gridded on a 2.5-degree grid, 144 x 73 cells (longitude x latitude) at different levels in the atmosphere, based upon their pressure. Hence, a two-dimensional slice of these data at a specific pressure level is organized in a torn mesh similar to that of the total column ozone, but at lower resolution and in a different geographic coordinate system. These data may also have gaps in coverage, including only a partial value for some wind cells (i.e., one or two of the three vector components are missing). For the data being examined, there are seven pressure levels (1000, 850, 700, 500, 300, 200 and 100 millibar [mb]).

If one considers the Mollweide cartographic projection discussed in equation (1), Figure 7 might be the result for October 1, 1987. Each of the seven pressure surfaces or slices of temperatures are independently used to define a cartographic warping, where the temperature is pseudo-colored according to a constant scale from 185 K to 315 K with isothermal contour lines every 5 K and overlaid with a coastline and national boundary map in the same manner as the ozone data were shown in Figure 4. Each of the seven Mollweide ellipses are stacked vertically according to a linear scale in pressure from 1000 mb to 100 mb, which can be seen in the axis. In addition, the opacity of each of the two-dimensional pseudo-color slices corresponds to the pressure height such that the 100 mb slice is almost transparent while the 1000 mb slice at the bottom is opaque. Since a pseudo-colored cartographic map is commonly used by climatologists to display two-dimensional data, Figure 7 could be viewed as an attempt to extend that traditional method to three-dimensional (i.e., volumetric) data. Unfortunately, it is perhaps only effective for viewing a small number of slices simultaneously.

Figure 7. Mollweide warped pseudo-color-mapped and contoured global atmospheric temperatures stacked by pressure and opacity-mapped for 1000 mb to 100 mb on October 1, 1987.

Alternatively, if one considers the spherical projection discussed in equation (3), Figure 8 might be the result for October 1, 1987. In this case, the temperature data are treated as a true volume by warping the parallelpiped mesh representation of the atmosphere into a collection of concentric spherical shells that compose a volume of 73,584 nodes. The temperature data are pseudo-color and opacity-mapped, but now direct volume rendered. At the center of the volume is a globe, which is created from the topographic data as in Figure 6. The radius of the globe is chosen to be the same as the inner radius of the spherical shell corresponding to the 1000 mb level. Although this picture may be interesting, little quantitative information can be derived. Hence, surface extraction techniques are appropriate for a more quantitative visualization.

Figure 8. Volume rendering of pseudo-color-mapped global atmospheric temperatures for 1000 mb to 100 mb on October 1, 1987.

Figure 9 illustrates these ideas for both the temperature and wind data on October 1, 1987. For the temperature data, surface extraction techniques are employed because direct volume rendering shows little quantitative information. The temperature data are realized as pseudo-color and opacity-mapped isothermal surfaces. The isosurfaces are at 194 and 294 K with the higher value (i.e., closer to the earth's surface) being more opaque. The pseudo-color spectrum on the left corresponds to that of the temperature isosurfaces. The wind data are realized via streamlines generated by numerically integrating the paths taken by injecting massless particles in the wind field at 150 points uniformly distributed within the volume. The lines are pseudo-color-mapped by horizontal speed ranging from 0 to 80 m/sec, which correspond to the pseudo-color spectrum on the right. The vertical component of the wind ranges from about -33 to about +45 mb/sec.

Figure 9. Isosurfaces of pseudo-color and opacity-mapped global atmospheric temperatures at 194 and 294 K and wind velocity streamlines pseudo-colored by horizontal wind speed for 1000 mb to 100 mb on October 1, 1987.

Further study of the data using these techniques shows that there is a region of cold air (i.e., around 200 K) over the Antarctic during this period that is concentrated near 100 mb in pressure height, that is surrounded by high-speed winds. The shape of this cold air mass and its diurnal variation at first glance appear to be similar to the depletion region in the total column ozone data. The shape of this air mass can be seen clearly in Figure 10. Two spherical, wireframe meshes surround a monochromatic globe. The outer green mesh of quads is at the 100 mb pressure level. The inner blue mesh of triangles is at the 200 mb pressure level. An isosurface at 194K is shown for October 1, 1987, which has two components, south polar and equatorial. The isosurface is pseudo-colored on a linear scale according to the pressure height at which the 194K value is determined. The pseudo-color scale ranges from blue (100 mb) to green (200 mb). Regions below 200 mb are colored pink. The south polar component of the isosurface is mostly at the 100 mb level. Hence, further study focuses on 100 mb data.

Figure 10. Isosurface of global atmospheric temperatures at 194 K isolated mostly at the 100 mb level on October 1, 1987, showing the signature of the polar vortex.

Correlating Ozone with Temperature and Winds

Two different approaches to visually correlating the ozone and dynamics data for the 100 mb level are taken utilizing the concept of coordinate warping to achieve geographic registration. The 100 mb data are the same as used in Figures 8, 9 and 10, and hence, are on a different grid than that of the ozone data. Since the aim of this study is to examine a phenomenon that is focused on a polar region and is nearly hemispheric in geographic extent, the orthographic cartographic projection discussed in equation (1) is utilized. They are illustrated using data from October 1, 1987 in an attempt to show the formation of the polar vortex and the ozone hole itself in Figures 11 and 12.

Figure 11 shows four separate and different data-driven representations of the atmosphere over the southern hemisphere in the same geographic coordinate system utilizing the same three redundant realization techniques: pseudo-color mapping, surface deformation and iso-contouring. This is the same approach as used for the ozone data in Figure 5, except for the addition of contour lines. In the upper left is the ozone column density with contours every 50 DU from 100 to 650 DU. The upper right shows the 100 mb temperature with contours every 5 K from 180 to 245 K. The lower left shows 100 mb horizontal wind speed with contours every 10 m/sec from 0 to 80 m/sec. Cells where one or more components of the wind velocity are missing are shown as gaps in this surface.

Figure 11. Southern hemisphere orthographic warped pseudo-color-mapped deformed surfaces with iso-contours of global atmospheric data on October 1, 1987: column ozone with contours every 50 DU from 100 to 650 DU (upper left), 100 mb temperature with contours every 5 K from 180 to 245 K (upper right), 100 mb horizontal wind speed with contours every 10 m/sec from 0 to 85 m/sec (lower left), normalized linear combination of column ozone, 100 mb wind speed and 100 mb temperature with contours every 0.5 from 0 to 3 (lower right).

In an attempt to show the correlation among these observable quantities in data space, a simple linear model is constructed such that

M = A O + B T + C |v|

where O is the normalized total column ozone ranging from 0 to 1 (scaled for the dynamic range of 110 to 650 DU),
T is the normalized 100 mb temperature ranging from 0 to 1 (scaled for the dynamic range of 180 to 245 K),
|v| is the normalized 100 mb horizontal wind speed ranging from 0 to 1 (scaled for the dynamic range of 0 to 80 m/sec),
M is a scalar field representing a unitless linear combination of the three parameters ranging from 0 to 3, and
A, B and C are normalized weighting factors, which are set to 1.

The ozone data are bilinearly interpolated to the grid on which the 100 mb data are available prior to the normalization. Independent gaps in both the ozone and wind measurements are properly maintained in the computation of M, which is shown in the lower right with contours every 0.5 from 0.0 to 3.0. Each of the surfaces shows a similar structure -- a depression of comparable shape and areal extent over Antarctica for low ozone, temperature and wind speed, respectively, each with a boundary corresponding to that of the polar vortex. The relative contribution of each of these parameters to the depression structure for M can be examined by interactively adjusting the weighting factors, A, B and C, in the computation of M.

Figure 12 combines each of the three different parameters into one visual object. As with Figure 5, both hemispheres are shown in the left and right sides of the Figure, respectively. The data are stacked vertically and shown with topographic, coastline and national boundary maps. The difference between Figures 12 and 5 are representations for the 100 mb horizontal wind velocity and temperature stacked between that of the ozone and the maps. Below the ozone surfaces are plates of vector arrows representing horizontal winds, whose direction correspond to the direction of the wind, and size and color correspond to wind speed, ranging from 0 to 80 m/sec. Below the winds and above the maps are flat, translucent planes corresponding to the 100 mb temperature realized as pseudo-color-mapped filled isothermal contours every 5K over the range of 180 K to 245 K.

Figure 12. Southern and northern hemisphere orthographic warped global column ozone as pseudo-color-mapped deformed surfaces, 100 mb horizontal wind velocity as vector arrows pseudo-colored by speed and 100 mb temperature as pseudo-color-mapped disks with contours every 5K on October 1, 1987.

A daily animation sequence from June through September shows the availability of polar ozone data as well as the formation of the depletion region in both presentations. A similar signature is visible as a blue region in the temperature data, before the ozone depletion occurs, as a cold air mass forms over Antarctica in the winter and persists into spring. A analogous but less well-defined shape forms in the wind realization. With the onset of spring, ozone observations become available and form a similar depression pattern to that of the temperature and wind. During this period, daily animation shows a clear rotation of the depletion region surrounded by the boundary of the polar vortex.

This rotation, which has a period of several days, is synchronous between the 100 mb and ozone data. The arrangement of the wind velocity arrows in Figure 8 evoke a cyclonic pattern corresponding to the polar vortex, that appears almost steady-state in the winter and early spring. By early November, the warming of the upper atmosphere over Antarctica is obvious with direct correspondence to the dissipation of the polar vortex in the wind data and the breakup of the ozone depletion region.

Although the four time-varying surfaces do show the correlation among the ozone and dynamics data, they are difficult to observe, especially in animation. The eye tends to focus on one or two of the surfaces only. Therefore, at the cost of obscuring some of the data, the stacked approach shows the synchronous circulation in each data set for the southern hemisphere during this period at single glance.