This material has been published in ICARUS 45, 398-414 (1981), the only definitive repository of the content that has been certified and accepted after peer review. Copyright and all rights therein are retained by the Academic Press. This material may not be copied or reposted without explicit permission.

 

Note on figures : The figures included in this HTML version of the paper have been reduced in size and resolution from the originals; as a result the labels on the axes are hard to read. The vertical axis on all figures is latitude (north pole at top), and the horizontal axis is aerocentric longitude (Mars season). Figure 1 goes from 0 to 360 degrees (ie one Mars year); all other figures have two years of longitude displayed. Figure captions give more detail on each figure. If better versions of the figures are needed, contact me at raethrasher@loop.com.

 

The Mars Water Cycle

(Copyright 1981 by Academic Press)

 

DONALD W. DAVIES

 

 Abstract

A model has been developed to test the hypothesis that the observed seasonal and latitudinal distribution of water on Mars is controlled by the sublimation and condensation of surface ice deposits in the arctic and antarctic, and the meridional transport of water vapor. Besides reproducing the observed water vapor distribution, the model correctly reproduces the presence of a large permanent ice cap in the arctic and not in the antarctic. No permanent ice reservoirs are predicted in the temperate or equatorial zones. Wintertime ice deposits in the arctic are shown to be the source of the large water vapor abundance observed in the arctic summertime, and the moderate water vapor abundance in the northern temperate region. Model calculations suggest that a year without dust storms results in very little change in the water vapor distribution. The current water distribution appears to be the equilibrium distribution for present atmospheric conditions.

 

 

The Viking orbiters started Mars observations in the summer of 1976 and have operated over a full Mars year, obtaining visible light images (with two 50-cm focal length vidicon cameras), temperature measurements of the surface and atmosphere (with the Infra Red Thermal Mapper) and measurements of water vapor in Mars' atmosphere (with the Mars Atmosphere Water Detector). This paper will describe a model of the Mars water cycle that attempts to explain the main features of the water vapor distribution and its seasonal change that have emerged from analysis of MAWD data, augmented substantially by IRTM, imaging, and radio occultation data also obtained by the Viking Orbiter spacecraft. For a description of the Viking orbiters experiments see "Scientific Results of the Viking Project," Journal of Geophysical Research 82, 1977.

Early observations (made during the Viking Primary Mission in 1976; Farmer et al.,1976) showed a surprisingly large amount of water in the arctic in the northern summer, with quite a bit of spatial structure correlated with surface albedo. Correlation of the measured water amounts with surface temperatures, obtained by the IRTM, showed that the atmosphere was near saturation. If the antarctic behaved the same way, then large amounts of vapor could be expected in the corresponding southern season (Davies etal., 1977). In fact an order-of-magnitude less water was observed in the antarctic, with basically no spatial structure.

In addition to the horizontal distribution of water, it was possible to extract from the water vapor measurements, through comparison with multiple-scattering calculations, the vertical distribution of vapor over the Viking I landing site. This laid to rest the popular belief that water vapor on Mars was concentrated very close to the surface, with a large fraction cycled in and out of the soil every day. The vertical-distribution analysis showed that the water vapor was mixed throughout the lowest few kilometers of the atmosphere (Davies, 1979a). Later comparison of atmospheric temperature profiles and measured water amounts showed that this was also true at other latitudes and seasons (Davies, 1979b).

The virtually flawless operation of the MAWD instruments for over a full Mars year has produced about 106 measurements of atmospheric water vapor for different latitudes, longitudes, surface elevations, seasons, and local times. Although each of these variables has some effect on the water amount, the major dependence is on latitude and season. For the purpose of comparison with the model calculations, the experimental measurements have been averaged over longitude and local time and have been binned into 100 latitude and LS intervals. (The aerocentric longitude, LS is basically the angle of Mars in its orbit around the Sun, measured from the northern spring equinox; i.e., at LS = 0 the sun is crossing the equator going north.) The observed water vapor amounts have been corrected for the effects of atmospheric opacity; however, this correction is probably not very accurate for 10-150 of LS starting at LS~205 and 2750 because of the very large opacity associated with dust storms at those times. Figure1 is a contour plot of the experimental results.

Fig.1. Longitudinally averaged measured water vapor amounts as a function of latitude and season (Ls). Units are precipitable microns of water (prmm)

In addition to the water vapor measurements a model of Mars water should account for what is known about the water ice distribution. The most obvious feature is the large permanent north cap, which was shown to be water ice by Viking orbiter measurement (Kieffer et al., 1976; Farmer et al., 1976)

The much smaller south permanent cap remains at, or near, solid-C02 temperatures all year long (Kieffer, 1979) and plays no significant role in the annual water cycle. It does not appear to be acting as a significant sink for water vapor in the summer (Davies and Wanio, 1981), and its cold temperature insures that even if it were composed of H20, and not C02, it would not act as a source. Viking 2 lander images (Carr and Evans, 1980) as well as water vapor measurement of regions near the edge of the retreating south annual cap (Davies and Wanio, 1981) suggest that there is some water ice included in the annual polar caps.

Another piece of information that is important to the understanding of the water distribution is the timing of the dust storms. When the northern hemisphere is having its "wet" season (the summer) the atmosphere has very little meridional mixing; when the southern hemisphere has its "wet" season the planet has episodes of intense meridional mixing (the dust storms). The annual seasonal temperature changes cause the amount of vapor the atmosphere can hold to vary, approximately 180o out of phase in the northern and southern hemispheres, causing a time-varying gradient in atmospheric water vapor to exist between the north and south. When the vapor gradient favors transport to the south, there is little meridional mixing; when the gradient favors transport to the north, the meridional mixing is large.

 

THE MODEL

 

The two most important processes that the model must account for are the meridional transport of water vapor and the change of state between vapor and ice. These are basically the fluxes of vapor into an atmospheric cell from the sides (the meridional transport) and the bottom (the sublimation from the surface). The condensation/sublimation of water will be controlled by the amount of vapor the atmosphere contains relative to its holding capacity, while the meridional transport will be assumed to be described by a meridional mixing coefficient (multiplying any vapor pressure gradient).

Basically the inputs to the model will consist of two major pieces:

(i)The holding capacity of the atmosphere.

(ii)The meridional mixing coefficient.

 

Both of these must be known as a function of latitude and season.

 

The Holding Capacity of the Atmosphere

 

Ideally the model should calculate water vapor and ice distributions with no input from experimental water vapor observations. The holding capacity of the atmosphere, here defined as the amount of water vapor the atmosphere can hold throughout the day, could be calculated from the temperature profiles of the atmosphere by taking the daily minimum of the integral of the saturation vapor pressure over a vertical column. Such temperature profiles exist (Lindal et al., 1979) but the coverage in latitude, season, and time of day, is rather sparse. Previous analysis of the water vapor data, and comparison to atmospheric temperature profiles, and temperature measurements made of the surface and atmosphere at 20 km, indicated that the northern temperate and arctic water amounts were near saturation most of the year, while the corresponding southern areas were saturated in the winter, but not in the summer (Davies, 1979b). Therefore, for those latitudes and seasons where previous analysis has indicated that the measured water amounts are near the atmospheric holding capacity (saturation), the measured amounts have been used. IRTM surface and atmosphere temperature measurements (Martin and Kieffer, 1979; Kieffer, 1979; F. D. Palluconi and T. Z. Martin, private communication) along with atmosphere temperature profiles from the radio occultation measurements were used to estimate holding capacities at other latitudes and seasons. As will be noted below, the holding capacity is only important at latitudes and seasons where the atmosphere is near saturation.

 

The Meridional Mixing

 

Although the meridional mixing of the atmosphere clearly depends on the latitude and season, there is little quantitative experimental data. During northern spring and summer there is a lot of structure in the water vapor distributions (often associated with variations in surface albedo) that persists for weeks at a spatial scale of a few degrees or smaller. This puts an upper limit (at least for the appropriate latitude and season) on the meridional mixing. At the lower end, there is atmospheric mass motion associated with the condensation/sublimation of the annual C02 caps which results in mass meridional motion of the atmosphere with a velocity of the order of 0.1 m/sec.

The upper limit translates to <10o of latitude per month, while the mass motion gives ~4o per month. The mixing coefficient chosen for the non-dust-storm latitudes and seasons, 2X1O5m-degrees/day, results in 5-10o latitude diffusion per month.

During the first Mars year of Viking observations there were two major dust storms at LS 205 and 275o These storms resulted in rapid mixing of the atmosphere over a large fraction of Mars in a time period of a few days. Dust from the first storm extended into the northern temperate region (Pollack et al., 1979), while dust from the second storm extended past the Viking 2 landing site and probably all the way to the arctic (Martin and Kieffer, 1979). Orbiter images (Briggs et al., 1979) and IRTM data (Peterfreund and Kieffer, 1979) show moderate dust storm activity in the southern hemisphere during the period between the two dust storms.

In order to account for the rapid atmospheric mixing during the time of the dust storms, the meridional mixing coefficient was increased for 5o of LS associated with each storm. The enhanced mixing extended to 30oN for the first storm and all the way to 900N for the second. The value of the mixing coefficient was increased to 1 x 107 m-degrees /day to produce planet-wide mixing in a few days. A somewhat lower value, 3 X 106, was used for the southern hemisphere between the two major storms to account for the many smaller storms during that time period. Note that the mixing coefficient input to the model has been derived from data basically independent of the water distribution data the model is attempting to reproduce.

In the model, Mars is divided into equally spaced latitude bands, each band consisting of an atmosphere and surface component. The atmosphere component is just the atmospheric vapor pressure (prm/m, precipitable meters of water per meter height) times the surface area of the band times the height of the atmosphere, taken here to be 10 km. This atmosphere component is basically the water vapor content of the band expressed as its ice equivalent in cubic meters.

The flux into a band from an adjacent band is equal to the difference in vapor pressure (prm/m) x meridional mixing coefficient (m-degrees/day) X circumference of the border between the bands (m) x atmospheric height (10 km) x step size (days)/latitude bin size (degrees).

The flux into the atmosphere from ice on the surface is proportional to the difference between the atmospheric amount and its holding capacity. The proportionality constant was arbitrarily chosen to result in a 5-day time constant for adding vapor to the atmosphere; the results are insensitive to this factor as long as the time constant is not large enough to impede seasonal changes. If the surface is devoid of water ice, or is at solid-C02 temperature (1500K) no sublimation is allowed. If the atmosphere has an excess of water (relative to its capacity) the excess is deposited on the surface.

In order to avoid "building in" the answer, the initial condition for the calculation was a uniform 40 prmm of water over the entire planet at LS = 0. The evolution of this distribution was followed at 2.5o latitude resolution for 1500 Mars days. Figure 2 displays the calculated amount of atmospheric vapor as a function of latitude and season. Even in the first 2 years, many of the qualitative aspects of the observed water distribution are apparent, in particular, the large amounts around the north pole. The calculated amount of water vapor in the southern hemisphere summertime is larger and has more time/latitude structure than experimentally observed.

Fig. 2. Model calculations of atmospheric vapor for two Mars years, starting with an initial 40 prmm total (atmosphere plus surface) at Ls=0. Black=0, white=50 prmm or more.

The corresponding ice amounts are shown in figures 3a and b. Initially most of the 40 prmm exists as ice, fairly symmetrically distributed between north and south. The first northern summer is warm enough to evaporate all of the surface ice, all the way to the pole, and the southern summer does the same. However, by the end of the second year, there has been enough ice deposited in the north to create a permanent ice deposit. The deposit in the equatorial region is transient and disappears after several more years.

Fig. 3. Surface ice deposits, same calculation as fig2. A:0-50 prmm; B:0-200 prmm

In order to completely get rid of the initial conditions, the model must be iterated for many years. Computations at 2.5o latitude resolution were too time-consuming to do this, so a run of l05 days(150 Mars years) was done at 5o resolution. At the end of this time the model had reached a steady state, repeating the same vapor and ice distributions every year; i.e., there was no long term net transport. The results of the 5o calculation were used as the initial conditions for shorter runs at 2.50 resolution.

Figure 4 gives a gray-scale representation of the final, steady-state annual distribution of atmospheric water vapor (for 2 Mars years). This represents the model calculation for a situation in which Mars repeat its atmospheric temperature variations and dust storms year after year with a pattern as observed during the Viking observations. In order to facilitate a quantitative comparison of the model results with the experimental data, figure 5 contains a contour plot of the model vapor amounts (heavy contours) and the model ice amounts (light contours). A comparison of the model vapor data in figure 5 with the experimental vapor data in figure 1 gives quite satisfactory agreement.

 

Fig. 4. Model calculations of steady-state atmospheric vapor: 0-50 prmm.

 

Fig. 5. Comparision of calculated atmospheric vapor and surface ice for steady-state condition. Atmospheric vapor -- dark contours; surface ice -- light contours

To understand the details of the water vapor distribution it is necessary to compare the model vapor and ice distributions. Figure 5 is two overlain contour plots-the vapor distribution (same data as figure 4) and the corresponding quantities of ice. It is immediately apparent that the large amount of water vapor in the arctic is derived from the fairly local evaporation of water ice in the annual cap. Most of the vapor recondenses into the annual cap at the end of the summer, with a bit of it being transported south. Note that the horizontal line at 80o is the computed edge of the permanent cap, and that the thickness of the cap is not determined by the model-it depends on how much water was given to the planet by the initial conditions. Part of the permanent cap evaporates in the summer and is replaced in the fall and winter.

In the south, the model also predicts water ice in the annual cap, although only about one half the maximum amount (30 vs 50 prmm) of the northern ice. The H20 ice in the southern hemisphere extends closer to the equator than the C02 cap. The quantities of ice in this southern temperate region are small, and its possible that some of the ice may be suspended in the atmosphere as a thin haze. The quantities in the north arctic are fairly large (~5O prmm) and could easily raise the surface albedo, consistent with the observations from Viking Lander 2. Note the absence of any permanent ice deposits in the antarctic.

Figure 5 represents the main result of the model for the Mars that we observed with Viking. It would be interesting to calculate how the water vapor distribution would behave under different climate conditions, for example, at a different time during Mars' orbital precession cycle. However, we do not have a good way of knowing the atmospheric temperature structure (for the holding capacity) or the meridional mixing under those drastically different conditions.

One case, that is not too far removed from the year observed, can be investigated. The annual global dust storms can be inhibited for a year or two to see what changes to the water vapor and ice distributions are created. Figure 6 shows the atmospheric vapor distribution for two Mars years without global dust storms and figure 7 displays the difference between a non-dust-storm year and our nominal Viking year. The only substantial differences occur in the southern summer when maximum water abundances in the antarctic are increased considerably in the years with no dust storms. Note that after the dust storm season has passed, the vapor distributions are essentially the same. This is consistent with our experimental observation that where comparison could be made between two Mars years, the measured amounts of vapor at the same location and season were the same even though it is likely that the year preceding the Viking observations had less global dust storm activity. There is a difference in the amount of surface ice, figure 8a,b (particularly a drop in the amount in the permanent cap), but we have no way of measuring it.

 

Fig. 6. Calculated atmospheric vapor for two years without dust storms : 0-50 prmm.

Fig. 7. Change in calculated atmospheric vapor amounts for years without dust storms. Black = 5 prmm less in non-dust-storm years; white=5 prmm more in non-dust-storm years

 

Fig. 8. Change in calculated surface ice deposits. A:Same scale as fig.7; B:-50 to+50 prmm

It is also interesting to study what happens if an excess amount of water is put into the atmosphere. Twenty precipitable microns of water were put in the band from -5 to -10o latitude and the consequences watched for 6 Mars years. Note that this is 0.25 km3, a fairly substantial quantity of water, and of the order that could be released by a moderate impact if there is subsurface ice. Within 2 Mars years there is little trace of the water in the southern hemisphere. The excess resides in the permanent north cap and in the north arctic as ice in the wintertime and vapor in the summer. This excess of ice and vapor associated with the north annual cap slowly decreases as it is deposited on the permanent north cap. In the case studied, the excess north arctic annual ice deposit amounted to a few precipitable microns and it decayed at approximately 1 prmm/Mars year.

 

 

DISCUSSION

 

It is important to note what went into the model as input, what the model computed, and how sensitive the results are to the input parameters.

In order to determine what effect varying the meridional mixing coefficient has on the calculated distribution, model calculations were performed with different base and dust storm meridional mixing coefficients. The base (non-dust-storm) meridional mixing coefficient can be varied about a factor of 3 before substantial changes occur in the calculated distribution; in general, an order-of-magnitude change up or down produces a seasonal water distribution that is a noticeably poorer overall match to the experimental data. An order-of-magnitude change in the base meridional mixing coefficient would also be inconsistent with the observations mentioned earlier that were used to determine its value. It is quite conceivable that at a few locations/seasons a different mixing coefficient would make the agreement locally better, e.g., the arctic springtime seems to match better with a smaller mixing coefficient.

The mixing coefficient between the major dust storms can be raised from the value used with no effect on the vapor distribution (it is high enough to mix the vapor in a time short compared to the time scale associated with the retreat of the south annual cap); lowering it an order of magnitude allows a buildup of vapor in the antarctic as the south cap retreats. This increase is not seen in the experimental data.

Likewise, raising the dust storm mixing coefficient has little effect on the distribution, lowering it by a factor of 50 affects the vapor distribution in the southern summer as discussed earlier under the effect of inhibiting the dust storms--a lowered mixing coefficient results in substantially more water vapor in the antarctic than is observed experimentally.

Arctic and antarctic nonsummer model water vapor amounts are entirely determined by the saturation amounts used as input to the program--at any latitude/ season where the model has ice on the surface, the computed vapor amounts will be essentially the saturation amounts input to the model, which for those latitudes and seasons were derived from measured water vapor amounts. Therefore, for the polar, nonsummer, seasons the agreement between model and experimental vapor amounts is automatic and does not provide any real test of the model. For latitudes and seasons with no ice on the surface, the holding capacity of the atmosphere plays no role in the model. Since the other input to the model, the meridional mixing coefficient, was determined from other data, the close agreement between the model and experimental results for ice-free regions of the planet strongly suggests that the model accounts for the major processes responsible for the observed water vapor and ice distributions. Additionally, no information was put into the model regarding the surface ice distribution, yet the model correctly reproduced the large permanent north cap and the presence of small quantities of water ice in the annual caps. (The small, asymmetric south cap is below the resolution of the model.)

If we accept the validity of the model, some important conclusions can be drawn.

(a) The Mars water cycle is currently controlled by the atmospheric temperatures in the polar regions (through the temperature dependence of the atmospheric saturation vapor pressure). This control is especially important in the fall, when it controls the deposition of ice on the surface, and the spring when it controls the evaporation of the ice back into the atmosphere.

(b) Meridional mixing causes some of the arctic vapor to reach the northern temperate regions in late summer, but it soon ends up back on the north annual cap due to normal mixing and also due to the enhanced mixing from dust storms.

(c) The presence of a permanent H20 ice cap in the north, but not in the south is a consequence of current (as opposed to past) climatic conditions.

(d) The presently observed vapor and ice distribution (again excluding the south remnant cap) are in equilibrium; i.e., if climate conditions stay the way they are now, so will the vapor and ice distributions. The vapor and ice distributions have a shorter time to equilibrium than do long-term climate changes. If the climate is not changing, then there is no net transport of water to or from the north cap (averaged over times longer than a year).

(e) The annual caps contain small quantities of water ice in addition to C02. Maximum amounts of about 5O prmm are found in the arctic, with about half that amount in the antarctic.

(f) A year without a dust storm does not result in any major change in the water vapor distribution except during the dust storm period. If there had been no dust storms during the Viking year we would have seen more water vapor in the southern arctic summer, with a large concentration near the south pole.

 

ACKNOWLEDGMENTS

 I would like to express my appreciation to F. D. Palluconi and T. Z Martin for access to Viking Infrared Thermal Mapper temperature measurements, and to F. D. Palluconi and R. W. Zurek for many helpful discussions. Part of this work was carried out while the author was at the Jet Propulsion Laboratory, California Institute of Technology, under Contract NAS 7-100, sponsored by the National Aeronautics and Space Administration.

 

REFERENCES

 

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