2006:069 CIV
M A S T E R ' S T H E S I S
Correlation of Subsurface Ice Content and Gully Formations on Mars
Testing the Shallow Aquifer Theory of Gully Formation
Jeanette Edlund
Luleå University of Technology MSc Programmes in Engineering
Space Engineering
Department of Applied Physics and Mechanical Engineering Division of Physics
Acknowledgements
First of all I am grateful for all the help I have had from Dr Jennifer Heldmann and Dr Chris McKay. They have both helped me during all phases of this MSc diploma work.
I also want to thank my examiner Prof Sverker Fredriksson at Luleå University of Technology for a careful reading of the manuscript. I am also grateful to the Kempe Foundation, which supported this work with a generous grant, on an initiative by Sverker Fredriksson and Ella Carlsson.
Abstract
This Master of Science diploma project in Space Engineering was performed at NASA Ames Research Center and is based on images from the Mars Orbiter Camera. Pictures taken by this camera onboard the Mars Global Surveyor show gully features resembling water-carved gullies on Earth. One theory of gully formation on Mars contends that the source of the water feeding the gullies is a shallow liquid water aquifer. Interestingly, the gullies tend to form in locations of relatively low ice content. The shallow aquifer theory was quantitatively tested by calculating the temperature and pressure of the Martian subsurface at the measured alcove base depths in order to determine if liquid water can exist at these locations.
Since the density and thermal conductivity of the soil depend on the amount of ice in the soil, the ice-to-soil ratio is an important factor. The thermal conductivity and density of the soil were calculated for the location of the gullies, assuming that the ice content in the soil would be the same at all depths down to the alcove base depth.
Around 59% of the gullies were found to fall outside of the temperature and pressure regime of liquid water at the alcove base depth when assuming an overburden consistent with the observed GRS ice content. However, it may be unrealistic to assume that the measured GRS ice content extends down to the depth of the gully alcoves. Therefore the thickness of a dry layer that must exist within the overburden column for the water to be liquid at the alcove base depth is estimated. These calculations build on the assumption that the soil has a fraction of overburden with dry and icy components where the icy layer has the same concentration of ice as measured by GRS. According to these calculations, liquid water could exist in approximately 81% of the gully locations.
Some 19% of the gully locations could not have liquid water at the depth of the alcove base because the required thickness of the dry layer exceeds the alcove base depth. For the gullies where liquid water cannot exist under the surface, no outstanding characteristics were found regarding the albedo, elevation, channel length and thermal inertia. However, all of these gullies had very shallow alcove bases.
It is possible that the gullies that could not have liquid water at the alcove base depth have been formed in a different way than the other gullies, such as melting ground ice, snowmelt or a deep aquifer source.
Table of contents
1 Introduction ... 1
1.1 Background... 1
1.2 Problem... 2
1.3 Purpose... 2
1.4 Delimitations... 3
2 Theory... 5
2.1 Gullies... 5
2.2 Phase diagram ... 6
2.3 Liquid aquifer theory ... 7
2.4 GRS measurements and ice on Mars ... 7
2.5 Pressure and temperature calculations ... 9
2.6 Thermal conductivity... 10
3 Methodology... 13
3.1 Data collecting methods... 13
3.2 Locating the gullies... 13
3.3 Gathering the datasheets ... 14
3.4 Worst and best case scenario ... 15
3.5 Testing of different layers... 15
3.6 Handling the plots... 16
4 Observations... 17
5 Analysis... 37
6 Discussion and Conclusion... 39
References... 41
1 Introduction
NASA’s prime goal has for a long time been to find extraterrestrial life. One interesting place to look is Mars. It is a planet close to us and it has many features similar to Earth.
All of us have heard the theories about little green men on Mars, but the life form that NASA is looking for differs a lot from the extraterrestrial life forms of TV series and movies. NASA believes that since water ice has been found on Mars it might be possible that liquid water exists as well. Liquid water is necessary for life here on Earth and it might also be necessary on Mars. Scientists believe that bacteria and other small organisms could live in liquid water on Mars.
This paper will not try to find proof of life on Mars, but it will try to confirm that liquid water exists or have existed on Mars. All the work has been done as an examination of the gully features on Mars, since it is possible that they have been formed by liquid water.
One theory suggests that a liquid aquifer is lying beneath the soil at the depth of the alcove base of the gully. At these depths the pressure and temperature differ from the ones at the surface where water will instantly boil or freeze. This paper studies if the water at the alcove base depth can be in liquid form depending on the ice content in the soil above. It also examines the differences of the thermal conductivity if the thickness of the icy soil layer varies.
1.1 Background
NASA Ames Research Center was established in 1939 as the second laboratory of the National Advisory Committee for Aeronautics (NACA). NACA changed name to NASA in 1958. NASA Ames Research Center (ARC) is located in Sunnyvale, California, USA.
During its earliest days, Ames was leading the development in all flight regimes. Ames even built a very sophisticated wind tunnel that can take full-scale models of aircrafts.
Today Ames Research Center is a leader in nanotechnology, biotechnology, thermal protection systems and human factor research. About 4000 persons are currently working at Ames.
One of NASA’s prime goals is to find life on other planets in our solar system and beyond. The search for extraterrestrial life has been implemented at a wide range of places and methods, including, above all, the planet Mars. In 1999 NASA confirmed that frozen water had been found on the surface of Mars. This was a great discovery, since liquid water is necessary for life as we know it.
In 2000 Malin and Edgett reported that they had found geologic features resembling terrestrial water-carved gullies on the surface of Mars using the Mars Orbiter Camera (MOC) that is mounted to the Mars Global Surveyor spacecraft (MGS). This raised the hope that it was possible that liquid water has existed in the past on Mars.
A wide spawn of theories that try to explain the incidence of these features have been suggested.
Mars Odyssey was launched into orbit around the planet Mars. The spacecraft has three main instruments onboard, THEMIS (Thermal Emission Imaging System), GRS (Gamma Ray Spectrometer) and MARIE (Mars Radiation Environment Experiment). These instruments are used to estimate the amount of ice in the Martian soil.
The origin of the gully features is investigated in this report, with the help of data from Mars Global Surveyor and Mars Odyssey.
1.2 Problem
Since it was confirmed in 1999 that frozen water exists on Mars it is most likely that liquid water have existed on the Martian surface when the pressure was higher than present atmospheric pressure. Today the problem is that the temperature is below 273 K (0˚C) and the pressure on Mars is below water’s triple-point vapour pressure of 6.1 mbar.
This makes it impossible for liquid water to exist on the surface of Mars (Malin and Edgett, 2000).
Geomorphic evidence suggests that the gullies were formed by fluid activity and relatively recent (within the past few million years), since there are no craters or signs of meteoroids on the gully features.
Since liquid water will spontaneously boil and/or freeze on the surface of Mars (Haberle et al., 2001) the process of gully creation seems to be more complicated than just having water flowing down the slopes of crater walls and other slopes on the Martian surface.
Several theories exist that try to explain the incidence of gullies on Mars. This report will concentrate on a theory suggested by Mellon and Philips in 2001. It suggests that a liquid water reservoir is buried at the same depth as the alcove base of the gully. The pressure at that depth will be higher than at the surface, so in that way liquid water can exist. This theory can also be applied to carbon dioxide (Heldmann and Mellon, 2003).
1.3 Purpose
By using the data from both Mars Global Surveyor and Mars Odyssey the theories that explain the formation of recent gullies on the Martian surface can be confirmed or dismissed.
Similar calculations to examine the temperature and pressure in the subsurface of Mars were done by Heldmann and Mellon in 2003. But the calculations were made without regard to the amount of ice in the soil.
The purpose of this paper is to see how the amount of ice in the soil affects the temperature and pressure at the alcove base depths of the gully features on Mars.
1.4 Delimitations
Studies of the surface temperature and pressure on Mars have been done earlier with the help of data from the TES thermal inertia at the Mars Global Surveyor spacecraft. Hence the thermal inertia measured by TES only characterizes the upper few centimetres of the Martian soil. The thermal inertia at the lower depths could differ from that at the upper centimetres. The thermal inertia and the soil density depend on the ice-to-soil ratio. These are factors not taken into account in previous calculations. Epithermal neutron flux from the Mars Odyssey will be used to calculate the ice-to-soil ratio. Gully features on both the northern and the southern hemisphere on Mars will be investigated in this report. All the data used in this paper are taken from measurements done by Mars Global Surveyor and Mars Odyssey.
2 Theory
This chapter will present earlier discoveries about gullies and also explain different physical theories used in this paper.
2.1 Gullies
Images from the Mars Orbiter Camera on the Mars Global Surveyor show gully features resembling the water-carved gullies on Earth. Figure 1 shows an MOC image taken in the northern hemisphere on Mars. The location is 270.64˚W and 58.79˚N. The gullies are located in the mid to high latitudes between 30˚ and 72˚ in both hemispheres.
Figure 1. Portion of the MOC image M1800658 located at 270.64˚W, 58.79˚N (Malin Space Science systems, 2005).
The gullies can be divided into three parts; alcove, channel and debris apron. The alcove is identified as the presence of an eroded theatre-shaped depression from which a system of V-shaped channels, or network of channels begins, as can be seen in Figure 2 (Heldmann et al., 2005).
The channels have a typical width of 10 metre. The debris apron begins where the channels are no longer narrow, and instead they become wider and disappear (Heldmann and Mellon 2003).
Figure 2. Schematic view of the gully parameters. ZR, ZAlcl, ZAlc2, ZChan1, Zapr1, ZChan2 and ZApr2 are ridge elevation, alcove head elevation, alcove base elevation, channel head elevation, debris apron head elevation, channel base elevation and debris apron base elevation. The alcove length (LAlc), channel length (LChan) and depris apron length (LApr) are measured as showed in the picture to the right (Heldmann and Mellon, 2003).
If one compares the gully features on Mars with similar features on Earth the gully channels on Mars are much shorter, with a length of about 500 metres. Another difference is that the channels on Mars in 80% of the gully systems do not reach the end of the slope. According to these data, the channel length does not depend only on the topographic conditions. Some channels do not have debris aprons, but instead taper to an end (Heldmann et al., 2005). As can be seen in Figure 2, the alcove does not start at the ridge. The distance from the ridge to the alcove base elevation varies between different gullies.
2.2 Phase diagram
There is a big difference between the atmospheric pressure on Mars and on Earth. As shown in Figure 3 the atmospheric pressure on Earth is around 100 kPa depending on the local weather conditions. At that pressure, and with the temperature range of Earth, water can be found in the liquid or solid phase. At Mars the atmospheric pressure is in most cases under the triple point of water. According to Figure 3 the water on Mars will be in the solid or vapour phase, depending on the temperature. Liquid water can be stable on the lowest elevations and at low latitudes, since the atmospheric pressure is higher here than the vapour pressure of water. The temperature at the equatorial regions can reach 273 K during the day. The gullies are however almost never located in these regions (Heldmann et al., 2005).
Figure 3. Water phase diagram showing the triple point and the solid, liquid and vapour phases.
Conditions on Mars are almost always under the triple point. The figure is out of scale (http://www.sp.se/metrology/temperature/bilder/fasdiagram1_en.gif)
2.3 Liquid aquifer theory
Several theories are suggested to explain the existence of these gully features. Many of them have been dismissed by Heldmann and Mellon (2003). One theory that cannot yet be dismissed is that it is water that has carved the gullies and that the water comes from shallow liquid water aquifers. This theory was presented by Malin and Edgett in 2000.
Figure 4. Schematic showing the proposed location of a principal liquid aquifer (Heldmann and Mellon, 2003).
It is also suggested that liquid carbon dioxide (CO2) has carved the gullies. Both liquid water and carbon dioxide will be examined in this paper.
The theory suggests that liquid water or carbon dioxide is trapped underneath compact rock layers. The top layer consists of dry insulating material such as soil or porous rock.
An ice-cemented plug located between the aquifer and the slope surface prevents the water to escape. Variations in the pressure and temperature on Mars create increased fluid pressure in the aquifer that will fracture the ice-plug and let the water emerge and carve gullies. For these liquid aquifers to exist, the pressure and the temperature at the depth of the aquifer must be in the phase of liquid water or for the CO2-case, liquid CO2
(Heldmann and Mellon, 2003).
2.4 GRS measurements and ice on Mars
In order to calculate the pressure and temperature at different depths in the Martian soil it is necessary to know the density of the soil. Since this depends on the amount of ice in the soil, the ice-to-soil ratio is an important factor. This factor can be calculated from the GRS data from Mars Odyssey.
The Martian soil is constantly exposed to cosmic rays from our sun and other stars. These have high energies and when they collide with atoms in the soil or the rocks they will release neutrons. The neutrons will then collide with other atoms nearby and excite them.
For the excited atoms to go back to their normal rest state they have to lose energy, by emitting gamma rays. Every element emits gamma rays with a specific energy. The energies of the emitted gamma rays reveal the distribution of different elements on the surface of Mars.
The GRS also measures the amount of hydrogen in the upper metre of the surface. Since hydrogen is most likely in the form of ice (NASA JPL, 2005), the ice-to-soil ratio can be calculated by the following Equation, that was presented by Feldmann, 2004. Here represents the mass fraction of water based hydrogen, Z is the neutron counting rate and the other constants are given in
20
MH
Table 1:
( ) .
2O = ⋅ p ∑ i⋅ i
H B Z A Z
M (2.1)
Table 1.
The values of the constants used in Equation (2.1), Feldmann, (2004).
Constants
B 1.061
p -1.567
A0 0.6991
A1 0.3291
A2 -0.1152
A3 0.01986
A4 -0.001651
A5 0.0000512
For the calculating of the thermal conductivity, the mass fraction of ice has to be converted to volumetric fraction of ice ( ), with the help of Equation (2.2) derived by Edlund, 2005,
O
VH
2
(2.2)
6. . 915 4
. 734
1650
2 2
2 ⋅ +
= ⋅
O H
O H O
H M
V M
Studies made by Paige (1992), Mellon and Jakosky, (1993) and Feldmann in (2004) have demonstrated that water ice at equatorial latitudes of Mars would be unstable unless isolated from the atmosphere. The water ice would be unstable within 45˚ of the equator.
Even though water ice cannot exist on the surface at that region the gamma-ray neutron spectrometer on Mars Odyssey still counts neutrons there. The most likely neutron reservoir is hydrated minerals. Some possible hydrous minerals including clays are zeolites, iron oxides/oxyhydroxides, salt hydrates and hydroxylates. These different minerals do not tend to form close to each other here on Earth, but since the footprint of Mars Odyssey is big it is almost inevitable that multiple terrains with multiple
possibilities for hydrate minerals are present at the same measurement. For each measurement the neutron spectrometer covers an area of 300,000 km2. That means that even if the deposits of the minerals are hundreds of kilometres apart they can contribute to a single measurement (Fialips et al., 2005).
2.5 Pressure and temperature calculations
The density of the soil depends on its ice content. The porosity of the soil is estimated to 40%. The density of icy soil and dry soil on surface level is 2018 kg/m3 and 1650 kg/m3 respectively (Heldmann and Mellon, 2003). The density of the soil will increase with greater depth because the pressure increases with depth. The density ρ of soil with an soil ice-to-soil ratio of up to 40%, which depends on the amount of ice in the soil, can be calculated with the following Equations:
(2.3)
, 1562 1650
, 6 . 915 1650
2 2
⋅ +
=
⋅ +
=
icecontent icecontent
soil CO
Osoil H
ρ ρ
(2.4)
where 915.6 is the density of ice in kg/m3 and 1562 that of carbon dioxide ice, also called dry ice.
Using this result and the density Equation, the pressure (P) can be calculated with:
(2.5) .
z g P =ρsoil⋅ ⋅
Here ρsoil is the soil density, g is the Martian gravity (3.71 m/s2) and z is the alcove base depth.
The temperature at these depths is calculated with Equation (2.6) below, but the thermal conductivity is unknown and has to be calculated before the temperature,
0. T k z
T q⎟⋅ +
⎠
⎜ ⎞
⎝
=⎛ (2.6)
Here q is the geothermal heat flux, k is the thermal conductivity of the soil, z is the alcove base depth and T0 is the surface temperature.
2.6 Thermal conductivity
The thermal conductivity depends on the ice-to-soil ratio as shown in Figure 6.
Figure 6. This plot of the thermal conductivity verses the ice content was derived from the Equation (2.7).
The temperature was assumed to be 273 K, the porosity 40% and conductivity through the solid portions of the grains 3 W/mK.
The bulk conductivity (k) can be expressed as Equation (2.7) (Mellon and Jakosky, 1997).
w i
i w
k k
k k k
0 0) 1
( −ε +ε
= (2.7)
Here kw is the conductivity through the solid portions of the grains, ki is the conductivity of the interstice and ε0 is the porosity. Since kw is unknown, the value 3 W/mK is assumed. Using values from TES for the thermal inertia (I), specific heat (c = 837 J/kgK) at the gully locations and the calculated values forρ and c, the conductivity of the ice-soil free interstice (ki0) can be calculated as in Equation (2.8). Since the measurement is done in the upper centimetre of the Martian soil it is assumed that the top layer consists of ice-
free dust, sand or rock. All the moisture in the upper centimetre is assumed to have evaporated.
(2.8)
) (
2
0 I c
k
i = ρtot⋅
The conductivity of the interstice can be expressed as in (2.9)
(2.9) .
) 1
( A i0 A ice
i f k f k
k = − +
Where ki0 is the ice-free interstitial conductivity, fA is the fraction of the cross-sectional area of the pore space by which heat conduction through the ice occurs, and the conductivity of solid ice is:
(2.10)
. 4685 . 19 0 .
488 +
= T
kice
Here T is the surface temperature at the gully location, and kice is in units of W/m2K if T is in K.
The thermal conductivity of carbon dioxide ice is assumed to be 0.015 W/mK. The quantity fA is calculated as:
(2.11)
. ε0
icecontent fA =
(Mellon and Jakosky, 1997).
The Equation above calculates the thermal conductivity for a homogeneous layer. If the total conductivity of several layers is to be calculated, the thermal conductivity and thickness of each layer must be included. In Equation (2.12) the different thermal conductivities has been taken into account, but not the thickness of each layer. This Equation can be used when all the layers have the same thickness,
(2.12)
1 . 1 ...
1 1 1
3 2
1 ⎟⎟
⎠
⎜⎜ ⎞
⎝
⎛ + + +
=
n
total k k k k
k
Here ktotal is the total conductivity, and k1, k2, k3 and kn are the thermal conductivities of the layers. If the layers have different thickness Equation (2.13) must be used to instead:
(2.13)
.
1 ... _
3 3 2
2 1
1 ⎟⎟⎠
⎜⎜ ⎞
⎝
⎛ + + +
=
n n fraction fraction
fraction fraction
total k
z k
z k
z k
z k
Now zfraction is the fraction of the total depth that the thickness of the layer represents (Urquhart and Hanson, 2005).
3 Methodology
This chapter explains how the goal of this work was reached.
3.1 Data collecting methods
Data from the gamma ray neutron spectrometer from 2001 Mars Odyssey, which was used for the calculations, can be downloaded from the NASA homepage. There is one problem with that data though; it is not processed and it is hard to convert the numbers from the datasheet to mass fraction of ice in the soil. Therefore the epithermal data were downloaded from http://pds-geosciences.wustl.edu/missions/odyssey/grsspecial.html instead. This datasheet is processed and Equation (2.1) can be used to calculate the ice-to- soil ratio. The data are from the 25.7 first days of 2001 Mars Odyssey. The datasheet contains longitude, latitude and epithermal data for both the northern and southern hemisphere of Mars.
All the data were then downloaded to a computer called Maja at NASA Ames. It used Unix as an operating system, and the programming language is IDL (Interactive Data Language). Several users can simultaneously connect to Maja, and program and run their program. All the programming, calculating and plots in this report were made on Maja through a SSH secure shell connection.
3.2 Locating the gullies
When the data were downloaded and saved in the right directory on Maja some adjustments to the dataset needed to be done. The coordinate system on Mars is not like Earth, where there is one specific way to read longitude and latitude. Mars has two different systems. MOC and MOLA. The data for the locations of the MOC images containing gullies were in MOC coordinates, and the data from 2001 Mars Odyssey were in MOLA. In both cases the latitude is the same. It goes from 90˚ to -90˚, starting from the northern pole and moving towards the southern pole. The longitude is different for the two coordinate systems. To change the MOC coordinates into MOLA, one has to subtract 180˚ from the longitude.
For several plots, only the data from the gully locations were needed. To create an array with the epithermal data from the gully locations as special program was made. All the programming was made in IDL. The data vector was divided into 8 equal parts since the total vector was too large for IDL to handle. Each part was run through the program to select the measurement that was taken closest to each of the locations of the MOC images containing gullies. The epithermal data from that location were then saved in another array. The locations of the MOC images containing gullies were collected by Ella Carlsson, (2004).
At this point there were two different datasheets; one that contained the locations for the
datasheet with the data for the first 25.7 days. These two datasheets were used for the calculations of the mass fraction of ice. From these data Figure 8-13 were plotted. At this point, even if one MOC image contained several gullies, the location of these gullies were counted as one gully location, since the ice content was assumed to be the same for all gullies at the same MOC image.
Figure 7. Overlay of water equivalent hydrogen abundances and a shaded relief map derived from MOLA topography. The mass percentage of water was determined with epithermal neutron counting rates using the neutron spectrometer onboard Mars Odyssey between February 2002 and April 2003 (Feldmann, 2004).
The results for the ice content at a few locations of Mars were then compared with a map, showing how the amount of ice in the soil changes with latitude and longitude, as shown with Figure 7 above. This work was done by Feldmann et al, 2004.
3.3 Gathering the datasheets
The thermal inertia, elevation, alcove base depth, surface temperature and albedo at the location of the MOC images containing gullies was collected with existing programs and datasheets at the Oparin computer in Colorado. But since in some cases several gullies could be seen in the same MOC image and the gullies could have different alcove base depth, the datasheet had to be changed. Data were then corrected by hand. As an example, if one MOC images contained 4 gullies, 4 different rows were created. The longitude, latitude, ice content, albedo, surface temperature, thermal heat flux, thermal inertia and conductivity through the solid portion of the grain were set at the same level, since the resolution of the measurements are too low to see any differences between two gullies in the same MOC image. But the alcove base depths are different for all of the gullies.
Since both the location of the gullies and the amount of ice in the soil had now been derived, the thermal conductivity of the soil could now be calculated. But first the mass fraction of ice had to be converted into volumetric fraction, since the Equation for the
thermal conductivity uses volumetric fraction and not mass fraction. That was made by Equation (2.2).
Statistics for the ice content in the soil such as minimum ice content, mean ice content and maximum ice content was also derived for both the locations of the gullies and the total surface of Mars.
The thermal conductivity of the soil, was calculated for the location of the gullies with Equation (2.8), it was assumed that the ice content in the soil would be the same at all depths down to the alcove base depth. The result of this calculation is shown in Figure 15. Then the pressure and temperature at the alcove base depths of the gullies were calculated with Equations (2.6) and (2.7).
3.4 Worst and best case scenario
In order to understand the range of the temperature and pressure for the water at the alcove base depth assuming a layer with constant ice-to-soil ratio, a best and a worst case were plotted. The first two plots were made with different porosity, one with the lowest possible value and on with the highest. Then two other plots were made, where the thermal heat flux was set to the start and end point of its range. The same thing was done for the thermal conductivity through the solid portions of the grains and the density of the soil. Then the values for these characteristics that made the temperature and pressure come closer to the liquid phase were set and plotted to make Figure 17. The same thing was done to create Figure 16, but in this case values that made the pressure and temperature as far from the liquid phase as possible were chosen. The first plot was the best case and the second plot the worst one.
One plot was also made that shows how the thermal conductivity changes with the amount of ice in the soil, with the help of Equations (8-12). All the units were treated as constants except for the ice content that varied between 0 and 40%. Figure 6 shows the result.
3.5 Testing of different layers
In order to get an understanding how the ice content affects the temperature and pressure at the alcove base depth, calculations were made for each gully to estimate the depth of a dry layer that theoretically had to lie on top of the aquifer for the water to be liquid.
These calculations were made using Equation (2.7) and the temperature 273 K, which is the melting temperature for water on Earth. The values for thermal heat flux, surface temperature and thermal conductivity of the soil were set to the calculated values for each gully location. The results are shown in Figure 19.
The maximum ice content in the soil required for the water at the alcove base depth to be liquid was also calculated, and the thermal conductivity needed for the water to be in the liquid phase. The result is shown in Figure 15.
At this point both the thermal conductivity for dry soil and the thermal conductivity for the soil with the ice concentration that was measured with the neutron spectrometer onboard 2001 Mars Odyssey was derived. In order to get the total thermal conductivity of the soil if two layers of the type explained above were placed on top of each other Equation (2.13) was used. Calculations were made of the thickness of the dry layer and the icy layer in order to have the assumed water in the liquid phase. The results were plotted in Figures 20-22.
3.6 Handling the plots
The same calculations were done but the ice content in the gullies located over the latitude of 60˚ and between -45˚and 45˚ of latitude was set to 0.
The images in this work are saved as BMP files within the IDL procedures. There are several problems with this method though, files are relatively large, and the plot save white on black. The figures are therefore worked at in Adobe Photo Shop, the colours were inverted, the actual plots were cut out and finally saved as JPG files.
4 Observations
The locations of the studied gullies are plotted in Figure 8. Each asterisk represents one MOC image containing gullies. The dataset contains data from both hemispheres, but there are more MOC images with gullies from the northern hemisphere than the southern hemisphere. The total number of MOC images containing gullies is 243, of which 137 are from the northern hemisphere and 106 are from the southern.
Figure 8. Each asterisk represents a MOC image containing one or several gullies.
Figure 9 shows the same dataset, but plotted as a histogram. It shows the fraction of images located at a certain latitude. Most gullies are located between 30˚ and 60˚ in both hemispheres.
Figure 9. The fraction of MOC images with gullies located at a certain latitude.
The majority of the gullies in the southern hemisphere are located between -40˚ and -30˚
of latitude. On the northern hemisphere the majority of the gullies are lying between 30˚
and 50˚. No gullies have been found below -80˚ and above 70˚ of latitude. There is an area between -20˚ and 20˚ from the equator that does not have any gullies at all.
Figure 10 shows the mass fraction of ice at all the locations of Mars where measurements were made the first 27 days.
Figure 10. The ice concentration with respect to latitude on the Martian surface.
The ice-to-soil ratio on the surface of Mars changes with latitude as shown in Figure 10.
Each dot represents a measurement. The plot has 259,200 dots. The ice-to-soil ratio is small where the gullies are located. The minimum amount of ice in the Martian soil according to the data used in this plot is 1.8%. The maximum value is 60%. The mean value is estimated to be around 8.5%.
Above 60˚ the ice concentration decreases. This has earlier been claimed to be a fault in the data set. The ice content above 60˚ of latitude will increase as it does on the southern hemisphere.
Figure 11 shows the ice content both for the locations of the MOC images containing gullies and for the whole surface of Mars.
Figure 11. Statistical distributions of ice concentration in the images. The dotted lines show the ice concentration at the gully locations and the solid lines the ice content over the whole surface of Mars, including the gully locations.
As can be seen in the histogram of Figure 11, the ice concentrations for the gullies are statistically different from those of the full Mars surface. The ice-to-soil ratio at the gully locations are below 40%, the majority is below 10% for the surface of Mars, the ice concentration can be as high as 60%. The majority of the ice-to-soil measurements are in the 0 - 10% region, as for the measurements for the gully locations.
Figure 12. Histogram showing the ice content in the location of MOC images containing gullies.
Figure 12 shows statistics of the ice content at these locations but with a higher resolution than in Figure 11. A majority of the values are within 4 - 7%.
There are some locations of the MOC images containing gullies that have a higher ice-to- soil ratio compared to what is presented here, but the fraction is so small that it is ignored. These gullies are located on the southern hemisphere near the south pole.
Figure 13. Phase diagram of water, given as pressure versus temperature. The asterisks represent calculations for MOLA images with a homogeneous layer of soil with the ice concentration calculated from the thermal inertia at the same location. The triangles represent calculations with the assumptions that the layer on top of the alcove base depth is dry.
Since the ice-to-soil ratio at the gully locations has been calculated, the temperature and pressure at the alcove base depth were calculated. This was done with Equation (2.6) and (2.7). Figure 13 shows the temperature and pressure at the alcove base depth for dry soil and soil with the ice content calculated with Equation (2.1).
In this case the soil was assumed to be a homogeneous layer with the same ice content and thermal conductivity through the whole thickness of the layer. The asterisks represent the calculations made with the thermal conductivity calculated from Equation (2.8) and the triangles represent calculations made assuming that the soil layer was dry. In the case with dry soil, the thermal conductivity was calculated from the results for the thermal inertia at the gully location.
The results were plotted on top of a water phase diagram in Figure 13. According to this plot, the water at the alcove base depth will be in the solid state for the case with icy soil.
If the soil was totally dry, the water at the alcove base depth would be liquid in approximately 70% of the cases and solid in the remaining 30%.
Figure 14. The thermal conductivity and ice concentration at the location of the MOC images containing gullies. The asterisks represent calculations made using the measured values at the gully locations. The triangles represent calculated values for the ice concentration and thermal conductivity needed for the temperature at the alcove base depth to be 273 K.
Figure 14 shows how the thermal conductivity changes with ice concentration at the locations of the MOC images containing gullies. The asterisks show for each gully location the thermal conductivity calculated for the icy soil with the ice concentration from the TES measurements. The triangles show the thermal conductivity and ice concentration needed for the water at the alcove base depth to be in the liquid phase.
It is evident that the thermal conductivity for the icy soil is higher than the one for the ice-free soil.
Since the temperature and pressure at the alcove base depth are not only depends on the ice concentration, calculations were made to see how the other elements in the Equations change the temperature and pressure. To get a range of the result, a plot of the worst and the best case was made.
Figure 15. The worst case of the ice content. The porosity was set to the value 7%, the density to
2557.5 kg/m3, the thermal heat flux to 20 mW/m2 and the thermal conductivity through the solid portion of the grain to 10 W/mK. The values used in this plot are estimated by Mellon and Jakosky, 1997.
Figure 15 shows the worst case. A change of the values of the porosity, density, thermal heat flux and the conductivity through the solid portions of the grains the values of the pressure and temperature at the alcove base depth change. According to Mellon and Jakosky, (1997), the porosity can have a value between 7% and 45%. Here the value of 7% is used, since that will increase the thermal conductivity. The same happens when a high value of the conductivity through the solid portion of the grain is chosen. The values can be between 0.5 and 10 W/mK. In Figure 16 the 10 W/mK was used. The thermal heat flux can vary between 20 and 45 mW/m2. The worst case would be a thermal heat flux of 20 mW/m2. The density used in the calculations Figure 16 was 2557.5 kg/m3.
According to Figure 15 water at the alcove base depth for the locations of the MOC images containing gullies will be in the solid state if icy soil is present. In the case of dry soil, most gullies will have liquid water. But still some 30% will have solid water.
Figure 16. The same as Figure 13 but for the best case. The porosity was set to the value of 45%, the density to 1512.5 kg/m3, the thermal heat flux to 45 mW/m2 and the thermal conductivity through the solid portion of the grain to 0.5 W/mK (Mellon and Jakobsky, 1997).
If the values for porosity, density, thermal heat flux and conductivity through the solid portion of the grain are changed to get to best case, the phase diagram look like in Figure 16.
Here the porosity was set to 45%. This changed the density to 1512.5 kg/m3. The thermal heat flux is set to 45 mW/m2 and the conductivity through the solid portion of the grains is set to 0.5 W/mK (Mellon and Jakosky, 1997).
In Figure 17, one asterisk is in the liquid phase. The temperatures are higher compared with the worst case. In the calculation for both the worst and the best case, the ice concentration for each gully location was not changed.
Figure 17. Plot showing the phase diagram for carbon dioxide. The triangular represent the temperature and pressure at each location of the MOC images containing gullies.
The calculations for temperature and pressure can also be made assuming that the ice is solid carbon dioxide, also called dry ice. Figure 17 shows a phase diagram of carbon dioxide and the temperature and pressure at the alcove base depth for each gully location.
The ice concentration is assumed the same as in the calculations for water ice.
According to Figure 17 the pressure and temperature at the alcove base depth will free the carbon dioxide into gas phase at all gully locations. The pressure is too low for liquid carbon dioxide to exist.
Since it is almost impossible for liquid carbon dioxide to exist at the depths of the gully alcove base, no further calculations were made. All the following plots were based on calculations made assuming that the element carving the gullies was liquid water.
Figure 18. The dry layer as a function of the alcove base depth. It is assumed that a homogeneous layer of dry soil lies on top of the alcove base. The negative values show the cases where the alcove base depth is to small too make the water liquid.
If a homogeneous layer of dry soil is assumed to lie on top of the alcove base, the thickness of this layer needed to raise the temperature to 273 K at the alcove base can be calculated. Figure 19 shows the depth to the dry layer. The thickness of the layer from the alcove base depth is first subtracted.
The negative values in the plot represent the gullies where the thickness of the dry layer is greater than the alcove base depth. According to the plot, for the majority of the gully locations the alcove base is thick enough for liquid water to exist underneath the surface.
In Figure 19 one dry layer was assumed, but according to the measurements made by the TES instrument, there is ice in the soil. Figure 18 illustrates calculations assuming that the soil consists of two different layers; one dry and one with the ice-to-soil ratio calculated earlier.
Figure 19. The depth to the dry layer as a function of alcove base depth, the negative values represent gullies where the alcove base depth is not deep enough for the pressure and temperature to be high enough for liquid water to exist. Two layers with different thermal conductivity were assumed to lie on top of each other.
The total thermal conductivity for the whole thickness of the both layers together were calculated with Equation (2.13) One dry layer and one layer with the same ice concentration calculated from the TES values were assumed.
Figure 19 shows that about 81% of the gullies can have liquid water at the depth of the alcove base. The other 19% do not have deep enough alcove base depth or low enough ice-to-soil ratio needed for the water to be liquid. The negative values represent the gullies where the alcove base depth is too low.
Figure 20. The depth to the dry layer at different latitudes. Two layers with different thermal conductivity are assumed. One layer that is assumed to be totally dry and the other to have an ice-to-soil ratio according to the TES measurements.
Figure 20 shows the depth to the dry layer according to latitude. Since the majority of the gullies in the data set are from the southern hemisphere it is hard to draw any conclusions about the relationship between the depth to the dry layer and the latitude.
Figure 20 just like Figure 19 shows how many gullies that have an alcove base depth deep enough for liquid water to exist.
Since the MOC takes pictures over a large area, a single MOC image sometimes can contain several gullies. In Figure 19 & 20 gullies on the same MOC image represent by one cube. In Figure 21 all the gullies are plotted.
Figure 21. Plot showing the depth to the dry layer for each gully in the data set. The x-axis represents the number of each gully in no specific order. The negative values show where the alcove base depth is too small for liquid water to exist.
Here the x-axis shows the individual gullies in no specific order. The y-axis is also here the depth to the dry layer assuming two layers with different thermal conductivity. Some gullies have a negative value for the depth to the dry layer. This means that the thickness needed for the water at the alcove base depth to be in the liquid phase is higher than the alcove base depth. A closer look reveals that some 20% of the gullies have an alcove base depth that is too low for the water in aquifer to be liquid if a totally dry layer of soil would lie on top.
Figure 22 shows a water phase diagram with marks for both icy soil and dry soil at the locations of the MOC images containing gullies. The triangular markings represent the case of a dry overburden. The asterisks represent the temperature and pressure calculated with the ice content calculated from the neutron spectrometer results.
Figure 22. Plot showing a phase diagram. The asterisks represent the pressure and temperature at the alcove base depth of each gully using the ice content calculated from the neutron spectrometer. The triangular markings represent the temperature and pressure calculated assuming that at dry layer of soil would lie on top of the alcove base.
Figure 22 has some asterisks in the liquid phase that in figure 13 lied in the solid phase.
You can see in figure 22 that there are triangular markings at the asterisks in the liquid phase. These gullies lie either between -45˚and 45˚ of latitude or above 60˚. At those areas the ice content was set to zero since water ice is not stable at the equatorial area between -45˚ and 45˚, and the measurements above 60˚ were not correct. That means that the thermal conductivity in those areas would be the same for the both datasets of gullies.
In Figure 22 a homogeneous layer of soil with a constant ice content not depending on depth was assumed for the asterisks. In Figure 23 the same assumptions were made as for Figure 19-21; two different layers of soil with different thermal conductivities. One layer is dry and has the same thermal conductivity as calculated from Equation (2.8) and one layer has a thermal conductivity calculated from the ice-to-soil ratio at that location. As in Figure 22 the ice-to-soil ratio is set to zero for gullies that are located in the area of unstable water ice and the gullies above the latitude of 60˚.
Figure 23. Plot showing how the thickness of the dry layer changes with the alcove base depth of the locations of the MOC images containing gullies. The x-axis represents the alcove base and the y-axis the thickness of the dry layer that was assumed. In the case of the gullies were the ice content was set to zero, the thermal conductivity was set to the same as was calculated in Equation (2.8). The solid line in the plot represents where the thickness of the dry layer is the same as the alcove base depth.
Figure 23 shows how the thickness of the dry layer changes with the alcove base depth of the locations of the MOC images containing gullies. The x-axis represents the alcove base and the y-axis the thickness of the dry layer that was assumed. In the case of the gullies where the ice content was set to zero, the thermal conductivity was set to the same value as was calculated with Equation (2.8). The solid line in the plot shows where the thickness of the dry layer is the same as the alcove base depth. All the gullies that lie to the left of the solid line have an alcove base depth too small for liquid water at the alcove base depth even if the soil is totally dry. Around 20% of the gullies lie to the left of the solid line. Figure 24 shows the locations of the gully formations that lie to the left of the solid line.
Figure 24. The location of the gullies that cannot have liquid water at the depths of the alcove base.
There are ten MOC images containing gullies that have too much ice in the soil or are too shallow for liquid water to exist at the depths of the alcove bases. In these MOC images there are 63 individual gully formations.
Three of the MOC images are from below -70˚ of latitude. At these locations the ice content is high. The other gully formations lie above 60˚. One is located on the northern hemisphere and the other nine MOC images are taken in the southern hemisphere.
Since the 63 gullies described above cannot have liquid water at the alcove base depth it is possible that they have been formed in a different way than the other gully formations.
In Figure 25 - 28 some characteristics of the gullies and the surroundings are shown.
Figure 25 shows how the different parts of the gullies are located. The upper dash represents the ridge, the triangles represent the alcove head, the diamonds are the alcove base, the squares are the debris apron head and the lower dash represents the debris apron base. According to Figure 25 the alcove base depth for these gullies is quite shallow. The total length of the gullies is small. Most of them have a total length less than 500 metres.
Figure 25: The ridge (upper dashes), alcove head (triangles), alcove base (diamonds), debris apron head (squares) and debris apron base (lower dashes).
Figure 26: Ice concentration at the location of the gullies that cannot have liquid water at the alcove base depth.
Figure 27: Thermal inertia at the locations of the MOC images containing gullies that cannot have water in the liquid phase at the depths of the alcove bases.
Figure 28: The albedo for the gullies that cannot have liquid water at the alcove base depth.
The ice content at the locations of the gullies that could not be formed by a liquid aquifer are plotted in Figure 26. The highest ice content at these locations is above 45%. The lowest is about 8% (there are some locations that have an ice content at 0% since they are located between -45˚and 45˚ of latitude). These values are high compared with the other gullies.
In Figures 27 & 28 the thermal inertia and the albedo of these locations are plotted. No special pattern or level of values is observed in these plots.
5 Analysis
If the source for the fluid suggested to have carved the gully features on Mars came from liquid aquifers, as suggested by Malin and Edgett in 2000, the fluid could not be liquid carbon dioxide. This is clearly shown in Figure 17 since the pressure and temperature at the depths of the alcove base are not in the liquid phase. The carbon dioxide is in the gas phase. Hence, if there would be carbon dioxide in the soil above the alcove base it would rise towards the surface. Then pressure become lower, and the temperature fall. If the temperature and pressure is low enough the carbon dioxide will reach the solid phase and freeze. So the phase of the carbon dioxide will depend on the current conditions, but the pressure is to low for liquid carbon dioxide too exist anywhere in the soil column above the alcove base.
If the liquid would instead be water, it is possible that up to 80% would contain liquid water at the depths of the alcove base. The temperatures at these depths depend on the thermal conductivity of the soil on top, which needs to be very low. The highest value for the thermal conductivity at a gully location that would raise the temperature to 273 K at the alcove base depth is under 1 W/mK. The thermal conductivity of the soil is sensitive to the amount of ice in to soil. As shown in figure 6 even a small amount of ice in the soil would raise the thermal conductivity markedly. When the ice-to-soil ratio is high the thermal conductivity does not change as much as if it was small. But in the case of liquid aquifers the thermal conductivity needs to be low, so just a little amount of water ice can exist in the soil.
The soil on Earth is usually not homogeneous at a depth of several hundred metres. The case would most probably be the same for Mars. Nothing is known about the soil, rock or sand layers under the Martian surface. The measurements for the thermal inertia made to calculate the thermal conductivity represents only the upper few centimetres of the soil, and the measurements of the ice content were made one metre down. Hence, under the depth of one metre one can only guess the characteristics of the soil.
In Figure 13 one homogeneous layer of soil was assumed to be on top of the alcove base.
There, the water in the assumed liquid aquifer is in the solid phase. So, if the soil on Mars would be homogeneous according to thermal conductivity and density, the gullies could not be carved by liquid water from a liquid aquifer. As mentioned earlier this approach is not realistic. Big scale homogeneous shapes and characteristics are unlikely to form in nature on Earth. It would most likely be the same for Mars.
One more realistic approach to the problem was made assuming that the soil on top of the assumed liquid aquifer was made by two layers with different thermal conductivity. It was assumed that one layer had the thermal conductivity calculated from the TES measurements and the other one would have the same thermal conductivity as calculated from the ice content. Figure 23 shows that this theory can work in about 80% of the cases. In the other 19% either the thermal conductivity of the soil is too high or the alcove
base is not deep enough. One suggestion to why 19% do not have the required alcove base depth is that the top layer might have eroded and blown away by the wind.
It seems as if the soil consists of more layers than two. It is also possible that one layer could be made from solid rock and another from dust and sand. The ice in the soil could also lie in the soil as big chunks instead of equally divided in the layer, as assumed in the calculations. Since the calculations for the total thermal conductivity do not depend on the order of the layers, the approximation of two layers can be good enough. The assumption of two soil layers supports the theory of the liquid aquifer.
There is another theory that supports that the fluid that carved the gullies was liquid water. The channel lengths are small compared to what they have been if the gullies were formed on Earth. The temperature and pressure outside the liquid aquifer are lower than inside. The water will move towards the gas phase and the solid phase. That will lead to a situation where the water constantly freezes and evaporates to the atmosphere. So the amount of water running down the slope will decrease the further down the slope it will get until all is gone. This can also explain why the gullies in some cases miss their debris apron (Heldmann et al., 2005).
