JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 95, NO. B2, PAGES 1495-1510,FEBRUARY 10, 1990
Winter Frost at Viking Lander 2 Site
THOMAS
SVITEK
AND BRUCE MURRAY
Divisionof Geological
and PlanetarySciences,CaliforniaInstituteof Technology,
Pasadena
A key question in the study of Mars is water exchange between atmosphere and surface on
daily, seasonal, and astronomical timescales. We believe that small-scale processesaxe a key for
enhanced understanding of the global water behavior of Maxs. The principal data for this study
of small scalepropertiesof the Martian surfacewere collectedby the secondViking lander (VL 2)
and by both Viking orbiters. The annual deposition and retreat of the frost layer were observed
in situ by VL 2. The frost is inferred to be H20 frost but with some properties suggesting a much
thicker layer than would be expected from the simple mass balance calculation. Our original
contribution is in consideringthe effect of cold trapping (frost redeposition)which has been
previously neglected and which enables us to reconcile all the observations with environmental
conditions. In addition, we believe that this study points to a more general phenomenon of cold
trapping in the Maxtian environment. Our study of the VL 2 observationssuggeststhat H20 frost
occursin two forms: (1) thin, almostcontinuous,eaxlyfrost and (2) muchthicker, patchy,later
frost. Both frost forms contain essentially the same total water content, but they cover different
fractions of the surface. The transition between the two frost forms occurs by recondensation at
local cold traps when solax insolation sublimates the first frost but the atmosphere is still too cold
to transport the resultant water vapor away. These cold traps axe created by shadowing from the
small-scale surface roughness,rocks, troughs, etc. This hypothesis hinges on the dispaxity between
local and long-range transport of water vapor by the atmosphere. The local transport is driven by
abundant insolation energy available at the time of transition. This results in a laxge fraction of
surface frost being redistributed rapidly into locally thermodynamically preferable locations, cold
traps. Long-range transport is constrained by the atmospheric caxrying capacity. At the time of
transition, the atmosphere is still cold, not far from its winter minimum, and is almost saturated
by residualwater vapor (5-8 precipitablemicrometers).Thereforeit cannotcarry muchadditional
water vapor to lower latitudes. This dispaxity delays the global transport of water vapor by the
atmosphere.
INTRODUCTION
not enoughwater vapor for sucha thick layer of H20 frost to
form simplyby condensationfrom the Martian atmosphere
A key question in the study of Mars is water exchange
[Davieset al., 1977].ThereforeWall arguedthat this phase
between atmosphereand surfaceon daily, seasonal,and
function interpretation indicated a CO2 not a H20 frost
tronomicaltimescales[Jakosky,1985]. The data from the
composition. Furthermore, there was only an increase of a
Mariner 9 and Viking spacecraftpresentconvincingevidence
that substantial
amounts of water modified the surface of
Mars in the past [Cart, 1986]. However,at present,observablewater exchangeis limited to the dynamic behavior
few precipitablemicrometers(at most) in the water vapor
content of the atmosphereas frost disappearedin late win-
ter. Later, Hart and Jakosky[1986]presentedheat balance
calculation. They concludedthat this calculation precludes
of the polar caps[LeightonandMurray, 1966]and to occaformation of the CO2 ice at this latitude and season and
sionalfrosts,fogs,andclouds[Christensen
andZurek,1984].
therefore argued instead for H20 ice as the Viking Lander
We believe that small-scaleprocessesare a key to enhanced
2 winter frost. However, this very important and critical
understandingof the global water behavior of Mars.
Theprincipal
data
forthisstudy
ofsmall
scale
properties
conclusion
hastobereconciled
withtheresult
oftheWall
oftheMartian
surface
were
collected
predominantly
bythe study.
HartandJakosky
[1986]
suggested
thatfrost
phosecond
Viking
lander
(VL2)(with
itsmore
poleward
loca-tometric
properties
canbeconsistent
with10gmofH20
tion)andbyboth
Viking
orbiters.
Theannual
deposition
frost.
Butwethink
thatthere
aretwoproblems
withthis
interpretation.First, the quoted5% increasein reflectance
and retreat of the frost layer were observedin situ by VL 2.
is smaller by about a factor of 10 as compared with the
At the time of the Viking project, it was concludedthat this
reflectance increase which we measured. This will require
frost representedthe southernmostedgeof the northern seafrost of thicknessmuch larger than 10 gm. Second, Hart
sonalpolarcap [Snyder,1979].However,the questionof the
that deviationsfrom Lambercomposition
(H20 or CO2 ice)haspersisted[Guinness
et al., and Jakosky[1986]suggested
tjan
behavior
of
Wall
[1981]
could
be explainedby a much
1979;Joneset al., 1979]and is addressed
here.
thinner layer than Wall proposed. But comparisonwith the
Wall [1981]publisheda studyof the opticalpropertiesof
the Viking Lander 2 frost. He showedthat the measured originallaboratorydata of Smith et al. [1969]showsthat
these deviations from LambertJan reflectance are by far too
phase function is consistentwith a thicknessof the frost
small to admit a possibilityof 10 gm frost layer.
layer on the order of severalhundred micrometers. There is
These contradictingconclusions
from Wall [1981] and
Hart andJakosky[1986]intriguedus, and we undertookthe
Copyright 1990 by the American GeophysicalUnion.
work reported here. Our conclusionis that the VL 2 frost
was H20 ice, concentrated by cold trapping due to local
roughness
at the VL 2 site and probablyon muchlarger scale
Paper number 89JB03428.
0148-0227/90/89JB-03428505.00
1495
1496
SVITEK AND MURRAY:
WINTER FROST AT VIKING LANDER 2 SITE
as well. This first conclusion
(H20 ice composition)follows is constrained by the atmospheric carrying capacity. At the
closelythe previousresultof Hart and Jakosky[1986].Our time of transition, the atmosphere was still cold, not far from
original contribution extending the previous work of Hart
its winter minimum, and was almost saturated by residual
and Jakosky[1986]is twofold: First, we have considered water vapor (5-8 precipitablemicrometers). Thereforeit
in depth the photometric data obtained by an VL 2 imaging
experiment and have been able to reconcile those with the
calculation of thermodynamic stability of VL 2 frost. Second, we have developeda more detailed model of the water
vapor transport in the boundary layer on Mars during the
frost sublimation and redeposition. This model is an en-
cannot have carried much additional water vapor to lower
latitudes. This disparity delayed the global transport of water vapor by the atmosphere.
In the next section of this paper, we present the environ-
mentalsettingof the observational
platform (Viking Lander
2) and summarizethe data usedin our study. In the third
hancementto a simplermodelof Ingersoll[1970,1974]and
Toonet al. [1980]derivedfrom terrestrialapproaches.
This
modelproducesasits consequence
a cold-trapping(frostredeposition)mechanismwhichhasbeenpreviouslyneglected
section, we describe the proposed concept and the physical
processesoperating at the VL 2 site. In the fourth section,
we present the quantitative tests to which we subjected our
hypothesis. In the fifth section, we discussextensionsof the
and which enables us to reconcile the "thick layer" results concept to other situations as well as its limitations and deof Wall [1981]with the thermodynamic
analysisof Hart and lineate possibletests using future data. Last, we summarize
Jakosky[1986].Our analysisof VL 2 frostissufficiently
com- of the concept of cold trapping at the VL 2 site and discuss
plete to lead us to argue that some form of cold trapping its implications.
must be a common
attribute
of the Martian
environment
in
general.
Our study of the VL 2 observationssuggeststhat H20
ENVIRONMENTAL
SETTING
The Viking Lander 2 landed on September 3, 1976, at
frostoccursin two forms:(1) thin, almostcontinuous,
early
Utopia Planitia, 47.96øN and 225.77øW. The landing site is
frost (Figure 2) and (2) much thicker, patchy, later frost
located on the ejecta debris blanket of the Mie crater about
(Figure 3). Both frost forms containessentiallythe same
total water content, but they cover different fractions of the
surface. The transition between two frost forms occurs by
recondensationat local cold traps when solar insolation sublimates the first frost, but the atmosphere is still too cold
to transport the resultant water vapor away. These lowerthan-average-temperaturecold traps are created by shadowing from the small-scalesurface roughness,rocks, troughs,
etc.
This hypothesishingeson the disparity between local and
200 km southwest. The lander sits on a boulder field, with
fine dust and sand as substrate and with no clearly visible
bedrock. The panoramic view from VL 2 northward is in
Figure 1. Besidesthe top priority searchfor life, the landers
conducted a seriesof meteorologicaland soil properties experiments. The following data were used during this study.
Frost Surface Coverageand Color
Two facsimilecamerason top of the lander body took al-
long-range
transportof watervaporby the atmosphere.The most 3000 imagesduringthe lifetimeof VL 2 [Guinnesset
localtransportisdrivenby abundantinsolationenergyavail- al., 1982; Arvidsonet al., 1983]. About 600 of thesewere
able at the time of transition. This resultsin a large fraction taken during the first and secondwinter and reveal the
of surfacefrost being movedrapidly into thermodynami- tracesof the frost (Figures2 and 3). A selectedfraction
cally preferablelocations,coldtraps. Long-rangetransport of theseimageswasusedby us (Table 1) for measurement
Fig. 1.
VL 2 panorama.
SVITEK AND MURRAY:
Fig. 2.
WINTER
FROST AT VIKING
LANDER :2 SITE
1497
Early continuous frost.
of the changesin frost surface coverageand in color as a
function of LB. The surfacecoveragemeasurementwas performed by visually inspecting the images and using a grid
overlay to estimate the frost coveredfraction of the surface.
The color changeswere measuredby extracting pixel val-
sensorwas included as a part of the more comprehensivemeteorologicalpackageand was measured at a height of about
1.5 m. The Viking orbiter infrared radiometer(IRTM) in
its 15-/zm band provided an indication of atmospheric tem-
peraturecorresponding
to a heightof about 25 km [Kieffer
ues (DN, data numbers)from the identifiedfrost spotson et al., 1977]. This is about the maximumaltitude where
the surface(Figure4). This wasmadepossibleby a sequence water vapor can make a noticeable contribution to the total
of imagesof the samearea taken in colortriplets (through atmospheric column under most of conditions. The possible
red, green,and blue filters), usually with the calibration exception is a temperature inversion which can happen untarget in the imageand at the samelocal time (Table 2). der either oneof thesetwo conditions:(1) a vigorousdust
This sequencewas taken during the both winters and the stormor (2) surfacecoveredby CO2 frost. At thesecondimeasurementwas repeated for both. The color change was tions, most of the water vapor can be stored at this altitude
measuredby comparing DN valuesof frost, calibration tar- of 25 kin. However, the seasonof our study is after the global
get, lander cover,and bare soil in three colorbands (red, dust storm, there is permanent CO2 frost deposit on the sur-
green,and blue). Only relative color change(comparing face, and the large-scalethermal inversionat this latitude
differentareasof frost) is requiredfor the sakeof the argu- and seasonis not supportedby VL 2 and IRTM data (temment in this paper. Absolute color information is difficult
perature of IRTM 15-/zm band is consistently lower than
to obtain
temperatureat the VL 2 site).
because of uncertain
calibration
of cameras and
poorly quantified effect of atmospheric scattering. For our
analysis, the relative color changeis important only at the
time of transition
between
two frost forms.
Measurement of the frost brightnessand color as a function of phaseangle could yield further cluesabout the Martian soil roughnessand frost depositionmode on the surface.
However,as theseare not directly relevant to this topic, they
are not pursued further here.
A tmoaphericTemperature
The synthesizedvertical temperature distribution of the
atmosphere and its diurnal variation above the VL 2 site is
depicted in Figure 5. It is basedon the following expression:
=
z
= +
ZXT= (T• • -2 T• •i.)
Temperature is a key parameter in any volatiles study. whereT(z) is the atmospheric
temperature,z is the altitude
The primary use of temperature data in our study was to (in km), Tstis the steadytemperature(withoutdiurnalvaricalculate the atmosphericholding capacity for water vapor. ation), A T is the diurnalexcursionfrom the steadystatein
The first sourceof atmospheric temperature data was the the thermal boundary layer, TVL is the ambient temperature
landeritself [Heaaet al., 1977]. The ambienttemperature at the Viking lander site, T, 5 is the temperature measured
1498
SVlTEK AND MURRAY:
WINTER
FROST AT VIKING
LANDER 2 SITE
TABLE 1. List of VL 2 Images Used to Study
Surface Coverageof Frost and Results
CE Label
Sol
Ls,
deg
Cover, Uncertainty,
%
%
22D180
22D181
21D198
22D209
22D213
22D220
21D224
21D232
22D249
22D253
21E008
21E016
22E033
22E037
21E048
21E056
22E073
22E077
22E085
22E088
22E128
21E153
22E169
21E187
21E192
21E194
22E211
21E215
22E230
22E247
22F011
233
233
245
245
245
257
257
257
269
269
281
281
293
293
305
305
317
317
329
329
353
365
377
382
382
382
389
389
400
406
410
251
251
259
259
259
266
266
266
274
274
282
282
289
289
297
297
304
304
311
311
325
332
338
341
341
341
345
345
351
354
356
75
85
70
60
85
70
75
75
70
85
85
90
90
85
85
92
65
65
40
50
25
20
15
20
25
15
5
10
3
3
2
25
10
15
20
10
20
10
10
15
10
10
5
5
20
10
5
25
25
20
30
10
10
5
5
5
5
3
3
1
1
I
21D184
21D186
21D192
21D193
22D199
22D203
22D227
22D231
21D233
22E035
22E038
22E039
21E040
22E045
21E048
21E049
21E050
22E051
233
233
233
233
245
245
257
257
257
293
293
293
293
305
305
305
305
305
251
251
251
251
258
258
266
266
266
289
289
289
289
297
297
297
297
297
85
75
70
75
50
40
40
30
60
70
75
80
80
85
85
85
90
70
10
20
15
20
20
20
10
10
15
25
25
15
10
10
10
10
5
10
The Figure 5 profile is for Ls = 325ø and latitude of 48øN,
values approximate for the Viking Lander 2 site at the time
of winter
frost retreat.
The thickness of the thermal
bound-
ary layer, the magnitude of the diurnal temperature variation near the surface, and the temperature profile are es-
timatesbasedon thesesources:(1) theoreticalcalculation
of Flasarand Goody[1975],(2) Generalcirculationmodel
(GCM) simulationof Pollacket al. [1981],(3) the spacecraftoccultationmeasurements
[Davies,1979b;Lindalet al.,
Fig. 3. Later patchy frost.
1979], (4) Mariner 9 Infrared InterferometerSpectrometer
(IRIS) atmospheric
temperatureprofiles(M. Santeeand D.
by the IRTM instrumentat 15-/•mband, and z0 is the thick- Crisp, personalcommunication,
1989), and (5) calculation
nessof the thermal boundarylayer. The atmosphericther- baseddiurnal variation of meteorologicalparameters at the
mal gradient is estimated by linear interpolation between Viking lander sites [Suttonet al., 1979]. The result is a
the Viking lander near-surfacemeasurement and the IRTM
compromisebetween the desire for accurate representation
25-kin
of the atmospherictemperature(particularlyregardingthe
measurement.
TABLE 1. (continued)
o
CE Label
Sol
Ls,
deg
%
%
21E052
21E054
22E055
21E057
21E058
21E059
22E071
22E075
22E078
22E085
22E088
22E091
22E092
21E094
22E095
22E098
21E099
22Elll
21El13
21El14
21El17
21El19
22E128
22E129
22E136
21E153
22E169
21E227
22E230
305
305
305
305
305
305
317
317
317
329
329
329
329
329
329
329
329
341
341
341
341
341
353
353
353
365
377
398
400
297
297
297
297
297
297
304
304
304
311
311
311
311
311
311
311
311
318
318
318
318
318
325
325
325
332
339
350
351
80
60
80
85
85
80
75
70
60
70
40
50
60
60
80
50
75
85
80
80
65
80
25
25
10
25
15
3
3
15
25
5
5
5
10
15
20
20
25
30
15
20
15
5
25
5
10
5
15
15
15
5
10
5
10
5
2
2
50
Cover, Uncertainty,
221057
221058
221059
221060
221061
221062
221063
221066
221067
221075
211093
221096
221097
221098
221099
221100
221101
221102
211105
874
886
898
910
922
934
946
955
955
955
960
967
977
987
997
100
101
102
103
233
241
249
256
264
272
280
285
285
285
289
293
299
305
311
317
323
329
334
40
40
50
70
85
85
85
85
80
85
85
75
75
75
70
60
60
55
20
30
30
20
15
10
10
10
10
15
10
10
10
10
10
10
10
15
10
5
221065
211090
211091
221094
955
959
959
960
285
288
288
289
60
80
65
70
30
30
15
20
sensitivity
ofwatervaporpressure
ontemperature)
anda re-
,..--,,
200
----
250
--•
:.
300
350
400
alistic assessmentof what is known about the atmospheric
, stateat this particularlatitude and season.
The constantthermalgradientwith diurnalperturbation
is not that much different comparedwith one of the best
sources
of temperature
profiledata: fromMariner9 IRIS
experiment
(M. SanteeandD. Crisp,personal
communi-
450
cation,1989). This data sethasa verticalresolution
of
about one scaleheightwhichhidespossiblethermalwave
propagating
upward(asseenin Vikinglandertemperature
profiles
duringentry). But we areinterested
primarilyin
diurnalvariations,not in the absolutevalueof atmospheric
500
Fig. 4. (opposite)Exampleof pixelretrievalprocesses.
,---,
----
l
1500
SVITEK AND MURRAY: WINTER FROST AT VIKING LANDER 2 SITE
Atmospheric
Water Vapor
TABLE 2. List of VL 2 ImagesUsed to Study
Color Changes of Frost and Results
CE Label
Ls,
Sol
White
Red
deg
221057
221058
221059
221060
221061
221062
221063
221066
221067
221096
221097
221098
221099
221100
221101
221102
233
241
249
256
264
272
280
285
285
293
299
305
311
317
323
329
874
886
898
910
922
934
946
955
955
967
977
987
997
1007
1017
1027
.9
1.0
1.0
.9
.8
.9
.9
.8
.8
.8
.8
.8
.8
1.0
.8
.8
2.7
3.2
3.1
3.0
3.0
2.9
2.8
2.8
2.9
2.8
2.8
3.1
3.0
3.2
3.2
Late
Early
Frost
Frost
.9
.9
.9
.8
.8
1.0
1.0
1.0
1.0
1.0
.5
.6
Laterweusedthethermalstructure
of theatmospheric
boundary
tocalculate
theatmospheric
holding
capacity
and
relative
humidity.
Results
aresummarized
in Figure6. The
following
expression
wasusedto calculatethemaximumcolumnabundance
of atmospheric
watervaporin the unitsof
1.8
1.9
1.6
1.3
1.1
1.0
1.0
.9
.8
1.0
1.0
1.0
1.1
1.1
1.5
1.6
precipitable micrometers:
Ah
=Pice
I•/ Pv[T(z)].e(-/r)
kT(z) dz
where
• isthemolecular
weight
ofwater,PiceistheH20 ice
density,
pvT) is thewatervaporsaturation
pressure,
z is
thealtitude,
andH istheatmospheric
scale
height
(assumed
constant
in ourcalculation).
The shaded
areain Figure6
representsthe variationderivedfrom the diurnal VL 2 temperature cycle.
Viking orbiter water vapor columndata from Mars At-
mospheric
WaterDetector(MAWD)arealsopresented
in
water vapor holdingcapacity. A pocket of warm air at 25
km altitude can potentiallycontainsubstantialamountof
Figure6. In addition
to thevertical
temperature
profile,
thesaturation
bywatervapor(relative
humidity)
depends
alsoontheverticaldistribution
of watervapor.In contrast
of strongwatervaporconwatervapor,but this doesnot meanthat this watervapor to the pre-Vikingsuggestions
is available for surface interaction on a diurnal time scale.
centration
in thebottomfewkilometers
[FlasarandGoody,
favorsa moremixedstateof
Further supportfor not considering
a potentiallocalized 1975],currentunderstanding
Watervapor
storageof water vapor at high altitudescomesfrom the fol- thewatervaporin the Martianatmosphere.
to mixuniformly
for at leasttwoscaleheights
lowingfeedback:a higherdegreeof subadiabatic
tempera- is expected
[Davies,
1979a].
There
may
be
someenhancement
ofrelative
ture profilewill createmorestableatmosphere,
thusdimin-
in thebottomfewkilometers,
butthisisprimarily
ishingthe effectof this high-altitudewater. On the other humidity
bydiurnalvariations
in thethermalboundary
layer.
hand, a closer-to-adiabatic
temperatureprofilewill enable driven
more vigorousvertical mixing, but the amount of available Atmospheresaturationnear the surfaceon a diurnal basisis
piecesof evidence:mornwater vapor will decrease.In both cases,this enablesus to hintedat by severalindependent
usethe simplifiedmodelfor verticaltemperatureprofileas
described above.
2O
,
'":"/./.:.???/i/ii?????::???/
/:
•'.e - 325
I
,::':'"':':.:?'
oI
2?0
014
0
150
1•0
170
180
190
200
ß [•:]
Fig. 5. Atmosphericvertical temperature profile and diurnal
I ..... I"""':'•'""':i:'""':':':':":'•'i
.... I
I
2eo
2•0
300
s•.o
T..
s2o
sso
I
I
•4o
sso
seo'
[dog]
Fig. 6. Atmospheric
holdingcapacityfor water vapor above
VL 2 site(in precipitable
micrometers).
Theshaded
regionisthe
daily variation as calculatedfrom the VL 2 ambient sensorand
variationin thermalboundarylayer.Minimumvalue(left bound- IRTM 15-•m temperature.The smallpeakaroundLs • 290ø is
ary of the shadedregion)wouldbe for the adiabaticatmosphere because
of the warmeratmosphere
duringthe second
duststorm.
starting with the temperature given by the ambient sensoron The irregularities
at the minimumboundaryat the late winter
VL 2. The profileconsideredin our study is a linear interpola- (Ls • 330ø) isaneffectofthelocalVL 2 meteorology.
Theother
tion betweenthe surfacetemperaturefromVL 2 andtemperature datasetin thegraphistheMAWDmeasurement
(averaged
data
at the 25 km altitude from 15-•m IRTM band. The extreme case pointsincluding
errorbars).It is importantto notethat during
(rightboundaryof the shadowed
region)is for the thermalinver- thelatewinter(Ls • 330ø),the atmospheric
watervaporcontent
sionduring a dust storm. This inversionis not considered
very doesnotriseasrapidlyasthe atmospheric
holdingcapacityfor
likelyat the time of our study (late winter).
water vapor.
SVITEK AND MURRAY:
WINTER FROST AT VIKING LANDER 2 SITE
1501
ingfogs[Jakosky
et al., 1988],diurnalopticaldepthvariation heightof only 1.5 m abovethe ground[Hesset al., 1977]),
are (1) the wind structuremeasuredduringthe
[Pollacket al., 1979],and temperatureinflection[Ryanand othersources
Shatman,1981].
landerdescent[SeiffandKirk, 1977],(2) GCM simulations
It can be noted that at the coldest period of the win- [Pollacket al., 1981],(3) Earth analogies
[Sutton,1953],and
ter (Ls < 300ø), the observedMAWD water vapor column (4) theoreticalcalculations[Holton,1979; Priestley,1959;
abundanceis higher than the one calculatedfrom the Viking Plate, 1971]. More detailswill be presentedin the relevant
lander surfacetemperature. This is due to the increasedat- subsectionon the physical processesof the proposedmodel.
mospherictemperature at altitude of 20-40 km due to the
However, there is important distinction regarding the caldust loading from the dust storms. Our model of the ver- culation of vertical transport of water vapor from the surtical temperature profile doesnot deal with this possibility, face to the atmosphere. On Earth, the greatest obstacleis
as mentioned above. This subadiabatic temperature pro-
file couldincreasewater vapor columnabundance,probably
combinedwith the transport from the lowerlatitudes. However, this effectbecomeslessimportantlater (Ls > 300ø)
becausethe atmosphere
clearssignificantlyand getscooler.
formedby the boundarysublayerjust abovethe surface(less
than Im). Once the water vapor getsabovethis sublayer,
then further vertical transport is relatively fast compared
with rate of saturationof the atmosphere
with water vapor.
Thereforea simpletwo-layermodelcan be used(Figure 7)
Also,water vaporat thesealtitudesdoesnot readilyex- (diffusionfrominfinitesource(surface,e.g.,ocean)to very
changewith the surfaceon the diurnaltimescale.Therefore largereservoir(atmosphere
abovethe boundarysublayer)
our calculationsdo not specificallyapply to the possiblewa- throughnarrowconduit(this boundarysublayer))[Brutter vapor which can be stored at these higher altitudes.
saert, 1982].In the first approximation,the rate of vertical
transport which dependson the relative humidity abovethe
boundary sublayeris not a function of itself. The transport
For the purpose of this study, it is necessaryto estimate aboveis fast enoughto diffusewater vapor away into higher
the vertical mixing and horizontal transport of water va- altitudes from above this sublayer. This keepsthe relative
por in and out of the Martian atmosphere. This is, as humidity abovethe boundarysublayeronly a slowlychangmight be expected, poorly known. In addition to the set ing function of the vertical transport.
The situation on Mars is quite different. The rate of subliof landermeteorology
measurement
(performedat the fixed
Atmospheric Transport
Earth
,
'
Fn,oo•[p(0)-p(h)]
atmosphere
....
PH20
FH:O
(Earth)
2.5
Fu2o
(Mars)
surface
Pu2o
(Earth)
= 10•
PH,O
(Mars)
Mars
\atmosphere
/
PH:O
surface
Fig. 7. Differencein boundary layer dynamicson Earth and on Mars. On Earth, the diffusionthrough the laminar
sublayerjust abovethe surfaceis the most limiting effect. The rate of diffusionthrough this layer doesnot depend
on itself becausethe large availableholdingcapacityof the atmosphere(evenin very humid environment)above
this sublayer. On Mars, situation is quite different (due to much lower atmosphericholding capacity for water
vapor). Thereforethe simpletwo-layermodel cannot be used.
1502
SVITEK AND MURRAY:
WINTER FROST AT VIKING LANDER 2 SITE
mation(controlled
byabsorbed
solarenergy)
issmaller
only culation,the critical parameteris the grain sizedistribution
by a factor of about 2.3 . But the atmospheric
water va- of the soil. We havetried to synthesize
severalindependent
por holdingcapacityis lowerby a factorof 104. Therefore pieces
of evidence,
namely(1) atmospheric
scattering
[Polit is mucheasierto saturatethe atmospherenear the sur- lacket al., 1979;Zurek,1982],(2) thermalinertia[Kieffer
face. A modelusedto calculatethe verticaltransportof et al., 1977; Jakosky,1986], (3) lander mechanicalpropwater vapor throughthe Martian atmospherehas therefore erties[Mooreet al., 1987],(4) dustsettlingafterlanding,
to take into accountthe implicit dependence
of the vertical (5) phasefunction
fromorbitandVikinglander,(6) geoltransport rate on itself. This then requiresuseof the multi- ogy arguments(presenceof dunesrequiressand saltation
layer modelwhichkeepstrack of differentlevelof saturation
throughout the atmosphere.
[SharpandMalin, 1984]),and (7) duststormarguments
(windnecessary
to pickup dustgrainsandlatersettling).
These considerationssuggestthe presenceof a bimodal size
Surface Temperature
Anotherimportantparameterfor this studyis surface
temperature.Thisis requiredto calculatethe froststability
on ground.Severalsources
of data wereoriginallysought
in orderto assurethe realisticunderstanding
of the surface
temperature. First, the Viking orbiter infrared radiometer
distribution
of dust/sand
particles:(1) veryfinedust(micrometerand submicrometer
size)whichconstitutesthe at-
mospheric
dustand (2) coarserparticles(hundreds
of micrometersin size,maybebondedtogether)whichconstitute
mostof themassof surface
material[Mooreet al.,1987].In
most cases, the diffusion properties of the material would
IRTM had a 20-/•mbandwhichgivessurfacetemperature be controlledby smallersize particles. Approximateanalaveraged
overthe fieldof view(typically40 km [Kiefferet ysis,as well as carefulcalculation,by Zent et al. [1986],
al., 1977]).Second,the footpadtemperaturesensoron the Clifford
andHillel[1980],Jakosky
[1983],Toonet al. [1980],
secondleg of the lander (J. Tillman, personalcommunica- and Flasar and Goody[1975]showsthat in this case,the
tion, 1989)provided
dataonthe surface
temperature
at the magnitudeof atmosphere/regolith
interactions(diffusion
in
VL 2 site. Third, we performedthe numericalcalculationof
regolith,adsorptionon regolith)will be negligibleon a diur-
surface
thermalbalance
basedonthe solarenergy,
thermal nal time scale.This, of course,appliesonly to the area and
radiation,andheatconduction
intothe ground(similarto time we havestudied(VL 2 winterfrost).
Kiefferet al., [1977]andothers).However,
aftercomparing
thesedata,we usedfor our analysisonlythe 20-/•mIRTM
PROPOSED MODEL OF COLD TRAPPING
measurements which we considered to be most reliable in
spite of the averagingeffect. Data from first two sources
A sketchof the proposedmodelis shownin Figure9.
(IRTM andfootpad)are compared
in Figure8. The foot- Our studyof theVikingLander2 observations
suggests
that
pad data are probablycontaminated
by the presence
of the
H20 frostoccursin two forms:(1) thin, almostcontinuous,
landerbody,a source
of thermalradiationandof shading early frost (Figure2) and (2) muchthicker,patchy,later
by the Sun. The conduction
of heat throughthe footpad frost (Figure3). Both frostformscontainessentially
the
was consideredto negligible.
sametotal water content,but they coverdifferentfractions
of the surface. The transition between two frost forms occurs
Diffusion in the Soil
by recondensationat local cold traps when solar insolation
We performedthis part of our study in orderto assure sublimatesthe first frost, but the atmosphereis still too
ourselvesthat the diffusion in and out of the soil can be cold to transportthe resultantwater vapor away. These
neglectedon the diurnal and subseasonalscale. For this cal-
cold traps are created by shadowingfrom the small-scale
210
2OO
V•-2
œoo•,p•:t
•.90
• •.•0
170
1•0
150
270
290
290
300
310
320
330
340
350
360
•'.. [d•g]
Fig. 8. Surfacetemperaturefrom IRTM (solidline) and VL 2
footpad sensor(dashedline). The diurnal minimum and maximum axeaveragedover 10ø of Ls (depictedby verticalbaxs).In
Fig.9. Caxtoon
ofthemodel.Twoformsof frost:(a) Eaxlyfrost
is a thin layer (10-20/•m), almostcontinuoussurfacecoverage.
(b) Laterfrostis a thickerfrost(100-200/•m),fractionof surface
the final analysis,only IRTM data were used, becausethe VL 2 ("coldtraps"). (c) Transitionis timing by surfacetemperature
footpadsensordata wereprobablycontaminatedby the presence (Ls • 315), limited atmospheric
transportprocessredeposition
of the lander body itself.
at locally favorable axeas.
SVITEK AND MURRAY:
WINTER FROST AT VIKING LANDER 2 SITE
surface roughness,rocks, troughs, etc. The critical feature
of the hypothesis is disparity between local and long-range
transport of water vapor by the atmosphere which delays
the release of water vapor into atmosphere. In order to
explain our model of H20 behavior, we must discussfrost
sublimation and condensation, surface thermal balance, and
water vapor transport in the boundary layer.
1503
quite analogousto the thermals found during hot days on
Earth [Ingersoll,1970]. This free convectionenvironment
does not practically limit water vapor sublimation; in this
casethe frost sublimation is limited by solar energy input.
Even if the situation described above requires in principle very little water vapor to decreasethe averagemolecular
weight of the gas,in the practical situation the inertial forces
will limit this phenomenonto rather high mixing ratio of waSublimation of Frost
ter vapor to carbon dioxide which in turn is possibleonly
Water on the Martian surface occurs in only two phases: at a temperature closer to the melting temperature. Theresolid and vapor. The solid and vapors are in equilibrium fore forced convectionis the most probable conceptfor the
if the partial pressure of water above solid ice follows this water frost sublimation at the VL 2 site. Knowledge of the
wind profile of the boundary layer is necessaryin order to
relation[Dorsey,1940]:
quantify this lossmechanism. Diffusion using an eddy mixA
log
[pv(T)]
= • + B.log(T)
- C.T+ D.T2- E[Pa]
where A =-2445.6, B = 8.23, C --0.01677, D - 1.2E-5,
and E = -7.781. This is independent of the total ambient
pressurecreatedby other gases(CO• in this case). The
transition from one phase to another is accompanied by the
release or absorbtion
of latent
heat:
= _
+c)
J
where A - 2.839E6, B - 3.6, and C - 35.
The water ice becomesunstable by either increaseof the
temperature of the solid phase or depletion of the vapor
phase above the ice. Kinetics of transition from solid to vapor phasecan be calculated in four possibleregimes: molecular flow, molecular diffusion, forced convection, and free
convection.
Molecular flow occurs at low temperatures where interactions between vapor moleculescan be ignored becauseof
low densityof the vapor. This can be a relatively rapid form
of sublimation limited only by energy input and the kinetic
ing coefficientrepresents
the simplestapproach(seelater in
this section).
Condensationof Frost
The opposite process to sublimation is condensation.
Careful understanding of this processis required for any
cold-trapping hypothesis. Water vapor is depleted from the
atmosphere by coming into contact with the surface at a
temperature lower than the temperature correspondingto
the water vapor partial pressurepv(T). This "coldfinger"
mechanismis complicated on Mars by the presenceof noncondensablegas, CO2. Therefore water vapor has to diffuse
in on the surfacefrom the CO• atmosphereand latent heat
has to get away, by radiation, conduction, or convection.
From the Earth analogs, we assumethe existence of a laminar sublayer in the boundary layer which has a thickness
severaltimeslessthan the typicalsurfaceroughness
[Priestley, 1959].The effectiveness
of coldtrappingdepends
onthe
rate of (1) heat transferthroughthis laminar sublayerand
(2) water vapormoleculardiffusionthroughthe samelayer.
First, the heat transfer rate is dominated by the radiative
transfer. This easilyremoveslatent heat releasedby the condensingwater vapor. The increasein surfacetemperature by
rate (• 10-•um s-• at the typicalVL 2 wintertempera- a degreekelvin will sufficeto remove latent heat generated
by watervaporcondensing
at therateof 2•umh-•. Thisfigure(2•um
h-•) isaboutthemostextremeupperlimit onthe
tures):
dh
I• ' pv(T) . y,h(T)
pv(T)
dt
ps ßkT
ps
frost depositionrate on the surface,and latent heat can still
be removedby only a slight increasein the surfacetemperature. Therefore
the removal of latent heat will not constitute
the limiting factor on the water frost condensationon the
surface. Second,the water vapor diffusion,through this laminar sublayer composedof a noncondensablegas, could be
the other limiting factor. The magnitude of a diffusion rate
can be estimated from x • • Dr. For D • 0.001m2s-• and
the frost (approximatelya few micrometers).On a larger x • i mm, we get t • i ms which is much less than would
scale, some of the following mechanismshave to be consid- be requiredfor any reasonablerate of water vapor condensaered.
tion. Therefore this analysisof water vapor condensationin
Molecular diffusion is important in the stably stratified the presenceof CO• suggeststhat the water vapor condenatmosphere or in the laminar sublayer which occurs just sationon colderspotsof the surface(coldtraps) will occur
abovethe surface(on scaleof 0.01-0.1 m). The coefficient at the rate controlled by supply of water vapor and will not
for the molecular diffusionof HaO through COs gas at the be limited by presenceof noncondensablegas.
where h is the frost layer thickness, •u is the molecular
weight, p• is the vapor pressure,yta is the thermal velocity
of vapor, p8 and p• are the solid and vapor phase densities. However, the conditions for this type of sublimation
are truly valid on Mars only in a very thin layer just above
Martiantemperatures
is typically0.001m
2 s-•. Thiswould
limit the water frost sublimation to only about 0.1 •um on
a diurnal basis; this is based on the typical molecular diffusion distance of 10 m in i day. The remainder of solar
energy input would go into increasedtemperature, leading
to correspondinghigher vapor pressure.
This situation will last until the lower molecular weight
Another
factor which should be included is the accommoon rock or
dation coefficient of water molecule condensation
ice surface. Unfortunately, the reliable measurementsperformed under the postulated Martian conditions are scarce,
and therefore this effect is not further quantified here. We
assume the value of accommodation
coefficient to be 0.8 as
we have no reason to believe that this value should substan-
of HaO (ascomparedto COs) causesunstablestratification tially smaller than unity.
1504
SVITEK AND MURRAY:
WINTER
FROST AT VIKING
LANDER 2 SITE
We have also consideredanother postulated mechanism essentiallyno laboratory data demonstratingthe effect of
for condensation,
on nuclei(dustgrains)in the atmosphere.grain size on phasefunctionof thin frost layers[Warren,
However, this cannot be important on a diurnal time scale. 1982],and thereforewe did not considerthe absenceof a
The fall-out rate for dust grainsis significantlymore than specular reflection to be a reliable indicator of thickness.
i day [Pollacket al., 1979]. Thereforethe amountof wa- SurfaceRoughnessand Water Frost Stability
ter frost deposited on the surface is not more than a small
Usingthe estimatesof solid/vaportransition,sunlightabfollows:a "precipitable"
layerof suspended
dust (1-5 •um sorbtion, and thermal emission,it is feasibleto calculate stafraction of micrometersper day. This can be estimatedas
bility of water frostdepositedon a surface.The temperature
1-3) timesthe ice/dustmassratioof nuclei(• 1) divided of the frost must be betweena minimum temperaturecorreby dustdecaytime scale(20-50 days).This mechanism,
in spondingto the partial pressureof water vapor in the atmoorderto be effective,wouldrequirevery largegrainswith un- sphere(for unlimitedwaterfrostsupply),and a maximum
realisticallythick water frost envelope.However,this mech- temperature correspondingto that a nonvolatile material of
anism may prevail during the initial depositionof frost on the same albedo as the frost would achieve due to solar inassumingmicrometersizedparticlesand optical depth •' •
the surfacein the late fall [Pollacket al., 1979]whendepo- solationandreradiation(for a fully saturatedatmosphere).
sition rates are 10-100
times slower.
Thermal Balanceof Thin Frost Layers
We assumethe horizontaldimensionsof the frost patch are
greater than the scalefor the horizontal heat transport from
the bare,darkersurfaceon the diurnaltime scale.(If this is
When describingthe thermal balanceof thin ice layers, not so,the stabilityof frostpatchwill be diminished.)This
severalnontrivial effectsmust be considered:albedo, ther- "critical" distanceis about 15 cm and is basicallyseveral
mal emissivity,
phasefunction.The effectiveness
of masking times larger than the diurnal thermal skin depth.
Another effectinfluencingthe surfacefrost stability is
underlyingcolor(i.e., red soil) of substratedependson the
surfaceroughness
createdby rocks,troughs,
froststructure(grainsizeand formof deposition)
as well the small-scale
as the thickness.Thereforea precisecalculationis very dif- etc. Small-scalesurfaceroughnesshas three thermal ef-
ficult,but experimental
data [Clark,1980; Warren,1982] fectswhichare difficultto modelprecisely:(1) the nonuni-
are consistentwith our assumptionsand measuredoptical form sunlightdistribution, (2) the subsurfacehorizontal
properties: The water frost layer thicknessof about 10-20 heat flow, and (3) the radiationshadowingof the surface.
•um(earlyfrostcovering
completely
the surface)
will not be Fortunately,for the purposeof our study,only the magni-
able to mask the underlayingred color of the substrate,so tude of these effectsis needed. A point calculation shows
the frostwill havereddishtint. The water frostlayerwhich that the net effectof roughnesson temperatureof parts of
is 100-200•umthick (whichis suggested
for the later frost surfacein shadow(potentialcoldtraps) is to moderatethe
in coldtraps)couldhavea largelywhitecolor,if we ignore temperaturesextremes. (On the other hand, the surface
which is more exposedto sunlightdue to roughness
would
a possibilityof contaminationby dust.
largertemperatureextremes.)This is dueto less
One interestingsuggestion
is the solidstate greenhouseexperience
duringthe day (lowermaximumtemperature)
as
effectcausedby solarheatingbeneathan ice layer. How- insolation
ever, the key argument is that no significanttemperature well as due to smallerexposureto the coldspaceduringthe
gradientcan be sustainedby sucha thin layer, as can be night henceleading to smaller lossesby thermal radiation
shownby a simplenumericalanalysis(B. Jakosky,personal (higherminimumtemperature).
This concept can be further extended and the effect of
communication,
1989).
In addition to this effect, the reversephenomenonhas to
be considered
aswell, whichwe call "inverse"greenhouse
effect lackingbetter terminology.By this, we meanthe effect
of thinnessof the frost layer on thermal emissionfrom the
frost. Becausethe frostchangesthe colorof the surface,it
has to absorbsomefraction of sunlight. However,the expectedearly frostthickness(10-20 •um)is aboutthe same
as a thermalwavelength.This couldcausethe emissivityto
be significantlylower than unity which would not allow the
small-scale roughnessbe estimated as follows: Let us as-
sumethat thereis a certainfractionof the sky (/•) which
is obscuredfrom the sunlight and at the same time radiation shadowed. Obviously,different spots on the surface
will have this insolation/thermalradiation pattern differently. However,averagingover the diurnal skin depth and
averagingfor a large number of cold traps will causethis
shadowing/obscuration
factorto not varytoo much(aswe
haveconvincedourselves
by a numericalstatisticalanalyfrost to reradiate all the solar radiation that it receives in sis). Then we can introducethis factor into standardthershorter wavelengths.This excessenergywould have to be mal balanceequation,and quite simplemanipulationof the
conductedinto the underlayingsoil and thus would causea
heat diffusion equation will show that the random smallscale roughnesshas the similar effect as the increasein ther-
thermal gradientat the frost/soil interface. The frost will
be warmer than the soil, which is quite oppositeto what mal inertia I:
is normally understoodas a solid-stategreenhouse.However, as in the previousparagraph, any thermal effect will
The net effect of this increase of thermal inertia will be an
be negligiblefor sucha thin layer. But this impliesthat it
increasein frost stability, therefore a decreasein the overmay be quite difficult to seesucha frost layer in thermal all rate of sublimation. This is because most of the frost
wavelengths.
sublimationoccursduringthe peaktemperaturein the day,
Thin frost layer can alsohavea profoundeffect,in prinand this peak temperatureis lower for the higherthermal
ciple,on the phasefunctionin reflection.There are sugges- inertia.
tions[Smithet al.,, 1969]that thin frostlayers(lessthan
about 200 •um) can exhibit a substantialspecularreflection peak. This is to be compared to the Lambertian re-
flectionof more massivelayers. Unfortunately,there are
Calculated Frost Thickness
In our work, we have used a simple one-dimensionalfinite
difference thermal diffusion model with the radiative
bound-
SVITEK AND MURRAY:
WINTER
FROST AT VIKING
ary condition on the top, with the latent heat contribution
from H20 sublimation and deposition, and with the proper
solar insolation geometry.
We have adjustedvaluesof the atmosphericoptical depth
and thermal infrared atmospheric downward flux until we
were able to replicate the IRTM surface temperature measurement. This was with no frost depositionor sublimation.
LANDER 2 SITE
1505
Third, the primary constraint on the behavior of water
frost at this site is overwhelminglythe atmosphericeffects
(i.e., vaporsupply,boundarylayermixing). Oncethe solar
energy input reaches sufficient level for the net water frost
sublimation, then in just a few days it can sublime more
water frost than we could ever expect in the continuousde-
posit on the surfaceat the Viking Lander 2 site. This is,
Thethermalinertiawaskeptconstant
at I = 6.5 (in unitsof of course,inconsistent
with the observed
behavior(wesee
10-3cal
cm-2s-•/•deg-•).Thenextstepwasto calculatethewaterfroststays
formuch
longer
thana fewdays,it is
the thicknessof water frost deposited/sublimed
usingthe stablefor up to 80 sols).
parametersfrom above. The frost deposition/sublimation The work describedin this sectionfollowscloselya previwas in the molecular flow regime, limited only by the en- ousstudyof Hart andJakosky
[1986].In addition,we have
ergy balance and the kinetic rate. Results are presentedin added the consideration of shadowed frost and further exFigure 10, which showsthe thicknessof depositedor sub- tended the model with boundary layer transport and frost
limed frost layer for two situations(frost in full sunlight, recondensation.We believethat thesethree effects(shadfrostin partial shadow)as a functionof LB. The valuesfor owing,boundarylayertransport,recondensation)
haveprothe frost in full sunlightis for the thermal inertia given above found implications for behavior of water at VL 2 site and
(I -- 6.5). The valuesfor the frostin partial shadowcomes possible at other locations.
fromthe modelwith the increased
thermalinertia (I = 7.7)
which corresponds
to • = 0.2 (obscuration/shadowing
of Boundary Layer Transport
sunlightis 20%, probablytypical for residualfrost patches
To deal with water vapor mixing and transport in the
at the VikingLander2 site). The frostdeposition
wascalcu- boundary layer adequately,we have striven to create a welllated from amount of latent heat necessaryto keep surface
temperature at a value correspondingto saturation pressure
of water vapor derivedfrom MAWD measurement.This, of
course,assumespractically unlimited supply of water vapor
from the atmosphere,which in turn would requirevery large
vertical mixing in the atmosphere.
Therefore we do not expect this calculation to yield realistic values for frost deposition and sublimation because
defined subset of assumptionswhich would be consistent
with the inadequately known structure of the atmospheric
boundary layer on Mars. The components of the wind in
the boundary layer are
u = <u)+ u'
w = <w>+ w'
we neglectedthe atmosphericeffects(limited atmospheric where(u>and (w>designate
the meanvelocityand u' and
transportand boundarylayermixing,seebelow). The val- w• designatethe deviationfrom the mean. We are considues in Figure 9 are overestimatedby a factor of several. But
the purpose of this exerciseis threefold. First, it predicts a
fairly accurate time when the net sublimation of water frost
exceedsthe net depositionand therefore when we shouldexpect the frost layer to break up. Second,it showsthat the
differencebetweennet sublimation for the fully illuminated
frostandshadowed
frostis about20ø L8 (whichis consistent
with the Viking Lander2 images).
tion will averageto zero ((w/ -0). We further assumethe
logarithmicwind profile[Holton,1979]for the surfacelayer
(the thicknessof whichis of the order of metersor tens of
meters):
(u)- •-ln -zo
where u, is the friction velocity, k is the Karman constant
experimentally determined to be about 0.4, z is the altitude,
and z0 is the roughnesslength. This length is approximately
an order of magnitude smaller than the physical size of sur-
so
40
ering only the two-dimensional model with horizontal and
vertical winds. We also assumethe vertical atmospheremo-
-
face roughness[Priestley,1959]. The friction velocityu,
defined as:
30
20
:to -
ax•b].].mMa].on
•* ----'•' 8
Ln a
where rx is the surface stressand p is the atmospheric density. The diffusioncalculation employsthe idea of an eddy
0
diffusion coefficient which can be estimated
-l.o
from
-20
K Oz- U,• K - k. u, . z - u, . l
--•0
where l is the mixing length. This surface layer with the
logarithmic wind profile extends to a height of about
-40
-$0
2';0
2•0
2•0
300
-•3.0
L•
a20
aao
a40
•0
a•o
[dog]
h • 0.2u__,
Fig. 10. Thickness of sublimed frost layer in one sol for two
differentsituations(frost in full sunlight,frost in shadow)as a
function of Ls. The calculation is based only on thermodynamical
balance and does not include mixing in the boundary layer and
cold trapping.
where f is the Coriolis parameter. Above the surfacelayer,
the eddy diffusion coefficient K in the Ekman layer is independent of height. This is the result of the assumption
1506
SVITEK
AND MURRAY:
WINTER
FROST AT VIKING
LANDER
2 SITE
1.0
:•ooo
18oo
16oo
14oo
12oo
• lOOO
0.0
800
ii
-
ii
ß
ß
600
ß
ß
ii
ß
ß
ß
ß
ß
ß
ß
400
_
X
200
X
.'1,•I15,11,1,.'1,•.'1;,
- O&,Cly
x x
x
o
o
I
•
2
•
x
I
e
e
o
20
40
eo
eo
lOO
Fig. 11. Syntheticatmospheric
profile,zonalwinds(w) and water vapor mixing coefficientK as a function of height.
•
ta o g • • • • a a a a
I
I
I
I
I
I
I
I
oa
I
I
I
I
0.0230240 250 260 2'70280 290 300 310 320 330 340 350 360
•w
[c•g]
Fig. 12. Changesof frost surfacecoverageand color as a function
of Ls. The solidsquaresare red/blue ratios from the red coloron
that the mixing length is proportional to the characteristic
scale of the turbulent eddies, which, in turn, is nearly constant with the height abovethis surfacelayer. On the other
end of the scale, mixing on the scale of surface roughness
dependson the existenceof a laminar sublayer. If
the VL 2 calibrationtarget (typically, around 3.0). The empty
squaresare red/blue ratios from the white color on the VL 2
calibrationtaxget (typically around 1.0). The crossesrepresent
the averagedcolor of the typical frost which disappeared quickly
around Ls • 325. The plusesrepresentthe color of the late frost
which stayedlongerand was getting "whiter" (lessred) during
the general disappearanceof most of the frost.
u,.--
z0
> 2.5
then we can talk about the aerodynamically rough flow,
where viscous stress is smaller than eddy pressure forces
fromflowoversurfaceroughness
(thereeventuallyhasto be
some laminar flow just next to the surface but only micro-
scopically
thin). Basedon valuespresentedin Figure11, we
expect this to be the case for the Viking lander sites.
Values used for the calculation
are anchored at the bottom
by the lander meteorology measurement, at the top by the
GCM results, and partially by the lander descentwind mea-
either by a thicker layer of the water frost over red substrate
or by a purercomposition
of recondensed
frost(lessdust/ice
mixture).
It is interesting to compare the timing of the above mentioned transition from the full to partial surface coverage
accompaniedby color changesof frost. This transition occurred the first winter around Ls - 325ø and a few degrees
earlier the secondwinter. Note that in Figure 10 it is approx-
imately(within 5ø) the time whenthe sublimationcapabil-
surement.The syntheticatmosphericprofile is summarized
ity of sunlight reachesthe thicknessthat could be expected
in Figure 11, zonalwindsand water vapormixingcoefficient
of typical continuouscoveragefrost, 20-50 /zm. Therefore
as a function of height.
QUANTITATIVE TEST OF MODEL AT VL 2 SITE
wecanconcludethat the time of transition(asseenin imaging) coincides
with expectedtransitionderivedfrom energy
balance calculation.
In this section, we compare the environmental observations with expectationsbased upon our model. First, we
presentargumentsbasedon the changesin frost surfacecoverage and its timing of transition as comparedwith frost
stability. Second,evidencefrom the water vapor column
abundanceand the vertical transport in the Martian atmospherewill be discussed.
Also note the steep slope of the solar heat input and its
derived frost sublimation capability. It means that for a
large portion of winter, insolation substantially lacks the
energy necessaryto sublime a significantamount of water
frost. However, once it reachesthis capability, any realistic
FrostSurfaceCoverage,Its Color and Timing of Transition
Water Vapor in Atmosphere:Holding Capacity and Vertical
Mixing
frostlayerwill be sublimedveryquickly(withina few days)
and frost is stable only in sheltered areas, cold traps.
Changesof frost surfacecoverageand color as a function
Further tests of the model at VL 2 site can be based on
of Ls are plotted in Figure 12. Note the sharp transition
the
MAWD data on water vapor column abundance and its
from full coverageof the surfaceby frost to partial coverage (typically15%). There wereparallelcolorchangesof relation to the atmospheric transport of water vapor. Meridthe frostlayer(alsoFigure12). The disappearing
frostwas ianal transport of water vapor has to be limited for sublimed
getting redder. This can be attributed to breaking up the water vapor to be redepositedin local cold traps. Otherwise,
surfacelayer and seeingmore of the underlyingreddishsur- meridianal transport will advect water vapor equatorward
face. On the other hand, the frost which was "destined" to where it doesnot have to be depositedas a surfacefrost bestay(that is is the frostin the locallyfavorableareas,behind causeatmospheric holding capacity is large compared with
rocks,in troughs)is gettingwhiter. This can be explained amount of sublimed water vapor. Meridianal advection at
SVITEK AND MURRAY:
WINTER FROST AT VIKING LANDER 2 SITE
the boundarylayeritselfis quitelimited;water vaporhasto
get mixedin the atmosphere
abovethis layer. This requires
rather substantialvertical mixing of the water vapor toward
altitudes above the boundary layer. In reality, the vertical
mixingis limited at this latitude and seasonbecauseof close
to saturationof the atmosphere.For most of the winter, at-
1507
The "leakage"from the boundary layer upward, that is, a
lossfrom the diurnal cycleof cold trapping, can be estimated
as follows: a 0 probability that a water molecule will be
redepositedin a cold trap within one day is approximately
the product of (1) a a fraction of surfacecoveredby cold
traps, (2) a "sticking"coefficientfor water moleculein a
mosphere
at this latitude(VL 2 site)is saturatedwith wa- water frost (whichwe assumeat thesetemperaturesto be
1982]),and(3) the number
ter vaporduringthe nightandabovethe thermalboundary closeto one,about0.8 [Adamson,
duringthe day. Thisstatementis basedon the atmosphericof times a water molecule has a chance to hit surface. The
temperature
dataandonthe MAWD data (compare
Figures last factor is just a ratio of the diurnal vertical distance
5 and6). Therewereabout5-8 precipitable/•m
of water traveledby random turbulencemotion in the boundarylayer
in the total atmospheric
column(mostof it within the first over the eddy diffusionlayer thickness.Therefore
two scaleheights).This is alsosupportedby the evidence
of morningfogs[Pollacket al., 1979;Jakosky,
1985;Jakosky
et al., 1988]and temperatureinflectionat the landersites
[RyanandShatman,1981].
Figure 13 showsthe estimatedeffectof verticalmixing where w' is the averagedeviation from the mean vertical
of water into the almost saturated atmosphere. The figure velocity(• 5 m/s), to is the durationof the day, and K is
showsthe diurnal cyclein the water vapor columnabun- the eddydiffusion
coefficient
(• 102m2s-•, Figure11 and
dancefor a period of 10 sols. There is a rapid increasein Jakosky[1985]).For •r • 0.1 (typicalfor the VL 2 site), we
thewatervaporcolumnabundance
aroundnoonbecause
the get 0 closeto one (within a factorof 2).
0•-,
cr
ß0.8.
atmospheric
thermal
boundary
layerapproaches
itshighest Thenumerical
diffusion
model
(shown
inFigure13)with
temperature
then.Afterward,
thereisa slowdecrease
inthe the parameters
for mixingin the boundary
layerasprewatervaporcolumn
abundance
because
thethermal
bound- sented
in theprevious
section
givesa diurnalcoldtrapping
arycools
downandthewatervaporisredeposited
fromthe efficiency
equalto0.9andthusconfirms
theestimate
above.
atmosphere
backon the surface.There is alwaysa slight
secular
increase
in thewatervapor
column
abundance
due Conclusions
About
Quantitative
Tests
to an increased
temperatureof the wholeatmosphere
and
alsobecause
of slowmixing(leaking)of watervaporfrom
the boundarylayerto the higheraltitudeswherewatervapor is advectedequatorward.This rate of increasein the
watervaporcolumnabundance
is denotedby lineA.
Thereare threeprimaryconclusions
to be derivedfrom
the quantitativetest of our hypothesis
at the VL 2 site.
First, there is a transitionin frost surfacecoverageand
color. The timingof the transitionis consistent
with the
layerthickness
derivedfromthe amountof watervaporin
the atmospherebeforewinter frost formation (10-30/•m).
The timing of disappearanceof the frost in cold traps in
consistentwith the thicknessof 100-200/•m. The changein
color(fromslightlyreddishtint to, probably,"bluish"tint)
1.5
is consistentwith the fresh frost redeposition into cold traps
where it covers the mixture
of thin frost and dust.
Second, there is no comparable increase in the atmosphericwater vapor column during the transition, not until
about 20ø L8 later. In the meantime, the water had to be
stored somewherebecausewe see disappearanceof the continuous frost coverage. This is consistentwith the most of
water stored in the cold traps as a frost.
Third, there is not much chance of water vapor being ad-
vectedquickly(i.e., within a few sols)to the lowerlatitudes.
0.0
o
i
I
I
I
i
i
i
i
i
2
3
4
5
6
'7
9
9
•.'i.m,m [8,ol]
Fig. 13. Estimated vertical mixing in the boundary layer. The
approximatecalculationof the residualwater vapor contentin the
atmosphericboundary layer on a diurnal cycle. It is important
to note that the true sublimation
of the frost from the surface
by solarinsolationis the seculartrend of the curveaveragedover
The vertical mixing in the boundary layer of the almost saturated winter atmosphereis very limited, and therefore water
vapor cannot get into higher altitude and thus being transported globally. It has to stay close to the ground where
chancesof hitting the surface at the cold traps is close to
one on diurnal
time
scale.
From these three arguments, we can conclude that our
hypothesisabout cold trapping of water frost at the VL 2
site is consistentwith the quantitative tests describedin this
section.
severalsols(lineA). The immediatesublimation
rate (aroundthe
DISCUSSION AND CONCLUSIONS
noonon eachday) is muchhigher(line B, comparewith Figure
10),but mostof watervaporcondenses
backonthe surface(cold
trapping). This calculationdoesnot take into accountthe possiIn this paper we have presentedquantitative evidencefor
bility of free convectionduringthe warmestparts of a sol (very cold trapping at the VL 2 site. This evidenceconsistsof the
unstableatmosphere).The mixing in the boundarylayer would
frost surface coverage and color transition, timing of this
be faster with the free convection but still does not reach the rates
given by thermodynamicalcalculation.
transition, and limited vertical mixing and horizontal water
1508
SVITEK AND MURRAY: WINTER FROST AT VIKING LANDER 2 SITE
vapor transport. Moreover, we believe that cold trapping
must be a general property of seasonalfrost and therefore
CO• frost, (2) residualwater frost substratebelowthe seasonal CO• frost being released gradually as the surface
must be considered
slowlyheatsup, (3) observational
effectof clouds,(4) temporarywaterstoragein clouds,or (5) waterfrosttemporar-
the VL 2 winter
in order to understand
the evolution
frost and the surface environment
of
of Mars
in general.
One consequenceof the theory is an effective delay by
about 20ø of L8 in release of water which was condensedas
a surfacefrost during the winter. Indeed, the possibledifference between the latitude of the peak water vapor column
abundance and the latitude of the edge of the retreating
CO2 seasonalice cap may require a mechanismfor delayed
release of water. Both the surface temperature and water
vapor column abundance as a function of L8 are presented
in Figure 14 for the northern seasonalcap during the spring.
ily lockedin local cold traps created by small-scalesurface
roughnessas we have interpreted happenedlocally at the
VL
2 site.
The firstpossibility(seasonal
watervaporreleasefromthe
regolith)requireseitherunrealistichighregolithpermeability to repeatedlyreleaseseveraltens of precipitablemicrometers of water during the spring for many years or continuousreplenishmentfrom the atmosphereduring other seasons. The continuousreplenishment mechanismis based on
a rigorousmodel[Jakosky,
1983].However,we havedoubts
The surfacetemperature(uppercurve)is measuredby the about the initial assumptionof this model: the equalvalue
20-•m band of the IRTM instrument. The drop to 150 K of a diffusionconstantfor diffusionin and out of regolith.
surfacetemperature occursat the latitude of the edgeof the Somemodelsof microphysics
of diffusionof vapor through
seasonalCO2 frost. The boundary is not sharp becausethe regolith could yield higher values for a diffusionconstant of
data were binned in 2ø bins in latitude and averagedaround water vapor from the regolith as comparedwith the diffuMars in longitude. The water vapor column abundance data sionback into the regolith from the atmosphere.Therefore
(lowercurve)weremeasuredby the MAWD instrumentand we believethat further work may still be neededto decide
again averagedin 2ø stepsin latitude and around Mars in
about this possibledirectional asymmetry in the diffusion
longitude. The data in Figure 14 are an average for the
constant.
period of Ls - 50ø-60ø.
The secondpossibility (residual water frost substrate
graduallyreleased)falls far shortof providingthe observed
If we assume that the CO2 seasonal frost acts as a sink for
water vapor seenin the atmosphereduring the summer and
early fall, then we shouldexpect the edgeof the retreating
seasonalcap to behave as a source for atmospheric water
vapor. There could be, of course, no release of water vapor before the CO• frost retreats. However, once the CO•
sublimes,the water vapor should appear in the atmosphere
rather quickly and then be transported equatorward. Therefore the peak of water vapor columnabundanceshouldoccur
just above the edge of the retreating seasonalcap which is
not the casein Figure 14. However,the peak of water vapor
is southwardfrom the edge of the retreating seasonalcap
delay of water release.One sol is quite sufficientto raisethe
temperature of a sunlit fraction of the surface from 150ø K
to 190ø K (equilibriumtemperaturefor the latitudeof 65ø in
Figure 14). Thereforeit wouldbe quite difficultto usethis
explanationas basisfor the 35 sol delay. Also, there is no
evidencein Viking orbiter imaging to support the existence
of this water ice substrate below CO2 seasonalfrost.
The third possibility(observational
effectof watervapor
clouds)suffersfrom the fact that the polar hazesextendat
mostonlya fewdegrees
southof the polarcapedge[ChristensenandZurek,,1984].The difference
in latitudesin Figby about10ø in latitude,whichcorresponds
to the delayof ure 14 is largerthan that (about 10ø).
about 20ø L s, or 35 sols.
The fourthpossibility(waterstoragein clouds)doesnot
Thisis a globalphenomenon
andcouldarisefrom(1) sea- providea reservoirwhich would be large enough.The optito only
sonalwater vapor releasefrom the regolith, not from the cal depthof hazesis about unity whichcorresponds
1-2 precipitablemicrometersof water ice [Christensen
and
Zurek,1984].
200
25
Finally,thefifthpossibility
(thecold-trapping
modelproposedin this paper) seemsto be consistent
with all the observations. We, obviously,do not have a direct evidence,
only a set of circumstantialobservationsand physicalarguments as describedin the previoussection. And, of course,
we cannot exclude that a combination
:l.
OO
lO
of effects mentioned
above,possiblewith otherswhichwe did not put forth, will
providethe consistentexplanation. Still, the coldtrapping
of water due to small-scaleroughnesscould be the relevant
model for the global behavior of water on Mars.
,o
05o
o
55
60
65
'70
lai:ii:ucl•
'75
80
85
90
[d•g]
Fig. 14. Differencebetweenthe latitude of the peak water vapor
column abundance{as seenin the MAWD instrumenton Viking
orbiter) and the latitude of the edgeof the retreating CO; seasonelice cap {a sharp drop of IRTM surfacetemperature toward
This assertionis basedon the followingmodel: oncethe
water vaporsublimationbecomespossible(i.e., after disappearanceof the seasonalCO• frost), in a very short time
(• i sol)20 precipitable•m of watervaporcanbe released
into the atmosphere.However,the long-rangetransport is
limited, due to still relatively cold atmosphereand slowmixing throughthe boundarylayer. Thereforewater vapor can
be transported
onlyoverrelativelyshortdistances
(at most
few tensof kilometers).But the water vapor getsinto contact with surfaceduring the transport through boundary
layer, and it is redepositedback on the surface,preferen-
SVITEK
AND MURRAY:
WINTER
FROST
AT VIKING
LANDER
2 SITE
1509
tially at the colder areas created by the small-scale rough-
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may be interpreted in terms of water frost recondensation.
the condensate observed at the Viking lander 2 site on Mars,
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However, there are still some Viking orbiter measurements Jakosky, B. M., The role of seasonalreservoirs in the Mars water
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55, 1-18, 1983.
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66, 117-124, 1986.
Jakosky, B. M., R. W. Zurek, and M. R. La Pointe, The observed
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Jones, K. L., R. E. Arvidson, E. A. Guinness, S. L. Bragg, S.
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Acknowledgments:
We wish to expressour sincere thanks for the
Viking Lander imaging observations of sediment transport and
helpful discussion and suggestionsto Andrew Ingersoll, David
H20-condensates, Science,204,799-806, 1979.
Stevenson, David Crisp, Bruce Jakosky, Richard Zurek, David
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(ReceivedSeptember13, 1988;
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