In 1989, Timothy Parker and colleagues at the Jet Propulsion Laboratory began analyzing the topography of Mars' northern lowlands for evidence of shorelines that would indicate the existence of ancient oceans.    In 2001 Parker and Clifford published a paper (Ref. 1) that delineated their findings in a map (Figure 1) showing the locations of several proposed shorelines.    Later, in 2003, Carr and Head (Ref. 2) reported their opinion that more compelling evidence for ancient large bodies of water were to be found in the deposits on the northern plains.    In between and since, arguments have been presented for and against the former existence of oceans on Mars.

The proposed shorelines consist of discontinuous boundary contacts between land forms, thought to have been created by waves or water-related processes.    However, the elevation of the contacts varies enough that they do not support a shoreline interpretation under present conditions.    In addition, Carr and Head argued that some of the mapped contacts are of volcanic origin and so are not supportive of a shoreline interpretation.    Of course, shorelines could have been obscured or altered by later geological processes and there is evidence to this effect.

To test the idea that the proposed shorelines could have resulted from bodies of water, I needed a way to create an accurate three-dimensional model of Mars that could be manipulated and calibrated.    I created a virtual three-dimensional model of Mars with a superimposed "ocean" using ray-trace rendering.    I used POV-Ray (Persistence of Vision ray-trace program), a free application with powerful features available on several computer platforms.

Ray-trace rendering can be used to create photorealistic scenes of virtually any object and is regularly used in many of today's motion pictures in place of physical models.    A particularly useful feature of ray-trace rendering is the ability to wrap a graphical image around a virtual object.    For instance, a virtual sphere can be wrapped with a flat map image of planetary terrain to create a three-dimensional image of the planet.    An extension of the this feature is the ability to wrap a topographical map on the surface of a sphere to duplicate a planet's terrain elevations.    This feature uses a function called an isosurface.

The Mars digital elevation model, or DEM, is a gray scale image that displays Mars' terrain elevations as varying shades of gray, darkest areas are lowest and brightest areas are highest:

A ray-trace function called an isosphere is used to "wrap" the DEM around a sphere and create a topographic surface matching that of Mars:

Next, a terrain color map is wrapped around the isosphere to create a realistic image of Mars:

Then a blue sphere is superimposed, concentric with the isosphere, and sized to intersect the isosurface terrain model to simulate an ocean:

A requirement of the analysis is the ability to adjust the virtual ocean to try to fit the shorelines depicted in the shoreline map (Figure 1).    Carr and Head used MOLA 64 pixel/degree data and Generic Mapping Tools to draw contour lines accurately at the elevations of the spillway between the Utopia and North Polar Basins and the spillway between Isidis Basin and the north polar depression (Reference 3).    The accuracy of these two contour lines (Figure 2) provides two data points on which to base an accurate calibration of the Mars model.

Calibration is accomplished by projecting an image of the Mars model northern hemisphere onto the Carr and Head map and adjusting scale and registration until the two contour lines can be matched by setting the ocean sphere to the two values.    Subsequently, the ocean sphere was set to several other known elevations to test linearity of the model.

The Mars model is sized in units equal to the equatorial radius of Mars in kilometers.    Thus, by adding or subtracting values, the virtual ocean can be made to intersect the terrain at any elevation to check calibration of the model.    By adjusting the scale of the isosurface until both the inner and outer basins contour lines were matched, a calibrated model was produced (Figures 3 and 4)

Figure 3.    Inner basins 4.350 km below the Mars datum

Figure 4.    Outer basins 3.509 km below the Mars datum

To test the proposed shorelines depicted in the shoreline map (Figure 1) it must be converted to a polar stereographic projection that can be superimposed on a projection of the Mars model as was done with the Carr and Head map.

Because the shoreline map extends from 15 degrees south to 65 degrees north, it must be extended to the poles to allow an accurate conversion from cylindrical projection to polar stereographic projection.    That projection must then be scaled by matching its surface topography to the model. First, the shoreline map must be extended to the poles:

And then wrapped around the Mars isosphere:

Next, the northern hemisphere must be converted to a polar stereographic projection:

Then the Mars model northern hemisphere is projected onto it and the shoreline projection is scaled and registered.    Water is added with no bulge and the volume is adjusted so that identifiable depressions can be brought into agreement with the Mars model to match scale:

The ocean sphere in the model is, initially, a perfect sphere so it must be distorted to simulate a tidal bulge.    I considered two types of bulge, an equatorial or oblate bulge and a polar or prolate bulge.

If Mars, orbiting the Sun as an independent planet, once had a global ocean creating the proposed shorelines, the ocean would have been distorted by planetary spin to the shape of an oblate spheroid.

I also considered a prolate tidal bulge because of the possibility that Mars was once a companion to a primary body.    There are hypotheses dealing with this concept.

To convert a spherical ocean in the model, a scaling factor is used.    Using Cartesian coordinates, the shape of the ocean sphere can be adjusted in a controlled manner.

In these three images of an ocean sphere the Cartesian coordinates, x, y, z are represented by three red cylinders.    The vertical cylinder is designated as the y-axis and is also the polar axis.    The other two cylinders are the x and z axes.    All are used for scaling.    In the left image the sphere is unscaled, no tidal distortion (x, y, z = 1).

In the middle image, an oblate shape is created by scaling down the y-axis and proportionally scaling up the x and z axes (x = 1.1, y = 0.9, z = 1.1).

In the right image, a prolate shape is created by scaling up the y-axis and proportionally scaling down the x and z axes (x = 0.9, y = 1.1, z = 0.9).

All axes are scaled to retain a constant volume for the sphere.    This requires a minimal number of manipulations when adjusting the shape of the sphere.    The proportions used here are for illustration only.    The proportional values used in matching shorelines are considerably smaller.

The following images show oblate and prolate oceans without (left) and with (right) latitude displacement of the pole.    Topographic scale and tidal bulge are exaggerated.

Once the shape is created, the ocean pole can be displaced in latitude and longitude to place it anywhere on the planet.    This distorted shape will then intersect the topography differently from the way the spherical ocean did.

Using a polar stereographic projection of the shoreline map on the Mars isosphere, manipulation of the following ocean parameters can be used in an attempt to match the shorelines:

1.    The type and magnitude of tidal bulge.

2.    Displacement of the ocean pole in latitude and longitude.

3.    Adjustment of the volume of water in the ocean.

In several areas, terrain subsidence and uplift appear to have changed the elevation of the shorelines and lava flow incursions may have obliterated others.

The following figures show a best fit result for two of Clifford and Parker's proposed shorelines, Arabia and Deuteronilus, with polar and equatorial tides.

Several issues presented themselves as I was performing this analysis.

There is no doubt the reader will notice that I did not model any crustal tidal deformation, although I did consider possible crustal deformation on Mars.

One scientist, assuming an equatorial tide displaced by polar wander, wrote of crustal deformation due to changes in the spin axis - but relatively little crustal deformation.    He proposed pole positions ranging from 30 - 58 degrees north for Arabia and 66 - 84 degrees north for Deuteronilus.    In my model the pole positions are more precisely determined.    The pole location for an equatorial tide for Arabia is 80 degrees north and for Deuteronilus, 50 degrees north.

Parker and Clifford, in their paper, wrote:    "assuming that the statistical distribution of Noachian elevations resembled that of today, a minimum of ~26-32% of the planet's surface would have been covered with water and ice."    The graphic that accompanies this statement depicts water covering the same area as the Arabia ocean in this analysis.

Lacking a convincing argument for substantial crustal deformation, I opted to assume that the present elevations resemble those of the period when the oceans may have existed.

Much discussion has transpired regarding the characteristics of the proposed shorelines claiming that the shorelines lack the physical evidence of wave action.    Although, sometimes in the same breath, the writer admits that the final determination will require human presence on the surface.

And yet, the lines are equipotentials as though formed by a pooled fluid under the influence of gravitation and either a polar tide or an equatorial tide.

What if the "shorelines" are an artifact of large bodies of ice?    Was Mars inundated by large volumes of water?    If so, might that water have pooled and relatively quickly frozen before wave action could have an appreciable effect?

Alternatively, if Mars had little atmosphere at that time, there would have been little ability for wind to create waves.

In calibrating the model I endeavored to determine the accuracy of the MOLA digital elevation model (DEM) and, in the process, I realized that the DEM is the standard against which the other elements must be compared/calibrated.    Accurate registration and scaling of the overlaid images of the Carr and Head map and the shorelines map are important in determining the degree of shorelines match.

The elevation values given in available literature for Mars' topographical features often vary from one source to another.    Some are based on old information.    The values given for Olympus Mons, for instance, range from 21 km to 27 km, and are not always based on the Mars datum.    The MOLA DEM places the peak at 21.171 km.

The deepest point, the bottom of Hellas basin, given as ~7.152 km below datum based on atmospheric pressure, measures -7.6 km in the MOLA DEM.    Based on the results of all other measurements in the model, I trust the MOLA data although Hellas basin depth is well outside the range of interest for the northern hemisphere elevations.

The accuracy of MOLA data is given variously in available documents.    Several sources allude to an accuracy of less than a meter and this is clarified in several places as "about a half meter" and "40 cm".    This turns out to be ranging accuracy.    The absolute accuracy of topographic elevations (radius) is +/- 10 m with a precision/resolution of 1 m.    Horizontal accuracy is +/- 100 m (Reference 4).    These tolerances are well below the resolution of the model.

My thanks to Dwardu Cardona and Frederic Jueneman for their constructive reviews during the preparation of this analysis.

(1) "The Evolution of the Martian Hydrosphere:    Implications for the Fate of a Primordial Ocean and the Current State of the Northern Plains"

Icarus 154, 40-79 (2001)

Stephen M. Clifford, Lunar and Planetary Institute

Timothy Parker, Jet Propulsion Laboratory

(2) "Oceans on Mars:    An assessment of the observational evidence and possible fate"

Journal of Geophysical Research, Vol. 108, No. E5, 5042 (2003)

Michael H. Carr, U.S. Geological Survey

James W. Head III, Department of Geological Sciences, Brown University

(3) Private communications from Michael Carr and James Head.

(2008)

(4) "Rover Localization and Landing Site Mapping Technology for the 2003 Mars Exploration Rover Mission" (Page 9)

Submitted to Journal of Photogrammetric Engineering & Remote Sensing (2003)

Rongxing Li and Kaichang Di, Department of Civil and Environmental Engineering and Geodetic Science, Ohio State University

Larry H. Matthies, Jet Propulsion Laboratory

Raymond E. Arvidson, Department of Earth and Planetary Sciences, McDonnell Center for the Space Sciences, Washington University in St. Louis

William M. Folkner, Jet Propulsion Laboratory

Brent A. Archinal, U. S. Geological Survey