ASPECTS OF THE ATMOSPHERIC SURFACE LAYERS ON MARS AND EARTH S. E. LARSEN1 , H. E. JØRGENSEN1 , L. LANDBERG1 and J. E. TILLMAN2 1 Wind Energy Department, Riso National Laboratory, Roskilde, Denmark; 2 Department of Atmospheric Sciences, University of Washington, Seattle, U.S.A.
(Received in final form 28 December 2001)
Abstract. The structures of mean flow and turbulence in the atmospheric surface boundary layer have been extensively studied on Earth, and to a far less extent on Mars, where only the Viking missions and the Pathfinder mission have delivered in-situ data. Largely the behaviour of surfacelayer turbulence and mean flow on Mars is found to obey the same scaling laws as on Earth. The largest micrometeorological differences between the two atmospheres are associated with the low air density of the Martian atmosphere. Together with the virtual absence of water vapour, it reduces the importance of the atmospheric heat flux in the surface energy budget. This increases the temperature variation of the surface forcing the near-surface temperature gradient and thereby the diabatic heat flux to higher values than are typical on the Earth, resulting in turn in a deeper daytime boundary layer. As wind speed is much like that of the Earth, this larger diabatic heat flux is carried mostly by larger maximal values of T∗ , the surface scale temperature. The higher kinematic viscosity yields a Kolmogorov scale of the order of ten times larger than on Earth, influencing the transition between rough and smooth flow for the same surface features. The scaling laws have been validated analysing the Martian surface-layer data for the relations between the power spectra of wind and temperature turbulence and the corresponding mean values of wind speed and temperature. Usual spectral formulations were used based on the scaling laws ruling the Earth atmospheric surface layer, whereby the Earth’s atmosphere is used as a standard for the Martian atmosphere. Keywords: Mars, Pathfinder, Spectra, Turbulence, Viking.
1. Introduction The atmosphere of Mars is the first extraterrestrial atmosphere with in-situ measurements. As such it is of interest for meteorologists to understand its behaviour and compare with models and equations developed and used on Earth, and indeed such efforts go back to the advent of space faring, e.g., Golytsin (1969). The basis for these models and equations is founded on basic science principles. However, many of the additionally used approximations and parameterisations are based on implicit and explicit order-of-magnitude assumptions for the different processes, as they occur on Earth, or based on data sets obtained from Earth’s atmosphere. Hence it is interesting to consider the Martian atmosphere as a first control sample to test our atmospheric results from the Earth. In the following we shall focus on boundary-layer aspects of this Mars-Earth intercomparison, mainly based on Boundary-Layer Meteorology 105: 451–470, 2002. © 2002 Kluwer Academic Publishers. Printed in the Netherlands.
452
S. E. LARSEN ET AL.
results and analyses of Viking data from Tillman et al. (1994) and of the Pathfinder data from Seiff et al. (manuscript in preparation). However, first we shall consider what can be inferred from the basic atmospheric characteristics of the two planets.
2. Considerations from Basic Characteristics In Tables I and II are listed characteristics of the atmospheres of Mars and Earth. In summary, starting with the large-scale and climate aspects, the solar constant for Mars is only about 44% of its value for Earth, being reflected in the somewhat lower near-surface air temperature of Mars (−50 ◦ C versus 15 ◦ C on Earth). However, there is considerable overlap between the temperature bands of the two planets, on Mars the reported range is: −125 ◦ C to +25 ◦ C, while the corresponding range for Earth is: −80 ◦ C to +50 ◦ C. Also, typically a larger fraction of the solar radiation reaches the surface of Mars than the surface of Earth (up to about 80% versus up to about 50%). Hence, the surface net-radiation environments are more similar for the two planets than is expected from the solar constants. Also it is noticed that the density and composition of the Martian atmosphere are quite different from those of the Earth. The surface pressure of Mars is less than a hundredth of the surface pressure of the Earth, and the atmosphere is mainly composed of carbon dioxide, while Earth’s is mainly nitrogen and oxygen. Due to greenhouse effects the average temperatures are higher than the radiation equilibrium temperatures, with about 40 ◦ C for Earth and 10 ◦ C for Mars. Since the surface temperature at the winter pole falls below the condensation temperature for CO2 , enough of the atmosphere freezes out at the winter pole to change the pressure of the whole atmosphere by about 10%, see Figure 1. The relatively high eccentricity of Mars’ orbit results in differences in the amount of condensation at the North Pole and the South Pole winters, resulting in the characteristic variation of air pressure during the Martian year, as seen on Figure 1. Moving to the parameters controlling the characteristics of the planetary boundary layer, the largest difference is found in the air pressure (1015 hPa on Earth and 6–7 hPa on Mars) and density, a difference that in turn produces similar differences between the kinematic viscosity, heat conductivity and heat capacity for the air on the two planets. Important parameters like the acceleration due to gravity, the Coriolis parameter, the atmospheric scale height, the dry adiabatic lapse rate and the buoyancy parameter are all found to be almost disappointingly similar on Earth and Mars. All are within about a factor 2 of each other and often much closer. The importance of the low atmospheric density shows up both for the scales of turbulence and for the near-surface vertical temperature gradients. It becomes simpler when we notice as empirical information that the wind speeds on Mars and Earth seem to be of about the same magnitude, see Figure 1. Hence we can assume the characteristic velocity scale, U or u∗ , to be the same on Mars and Earth. Below
ASPECTS OF THE ATMOSPHERIC SURFACE LAYERS ON MARS AND EARTH
453
Figure 1. The Martian climate illustrated from TLL (1994). Sol averages of pressure, wind speed, temperature, and different measures of optical depth from the data processed from the first 669 sols at the sites of Viking Lander 1 and 2 (VL1 and VL2), The VL1 winds are from Murphy et al. (1990), while the optical depths are from Colburn et al. (1989). For temperatures are shown the maximum, mean and minimum temperatures for each Sol.
TABLE I Composition [% by volume] of Mars’ and Earth’ atmospheres. Gas
Mars
Earth
CO2 N2 O2 H2 O Ar
95 2.7 0.13 0–0.2 1.6
0.035 78 21 0–4 0.9
454
S. E. LARSEN ET AL.
TABLE II Parameters characterising climate and atmosphere for Mars and Earth. Parameter
Mars
Earth
Units
Solar constant Orbital eccentricity Axial inclination Length of day Length of year Gravity, g Atmospheric gas constant, R Typical surface pressure, p Typical surface density, ρ Typical surface temperature, T Scale height, H = RT/g Cp ρCp Kinematic viscosity, ν Buoyancy parameter, g/T Dry adiabatic Lapserate,
591 0.093 25.2 24.62 (1 Sol) 686.98 (667 Sols) 3.7 188 7 1.5 10−2 220 11 730 11 10−3 1.8 10−2 4.5 10−2
1373 0.017 23.4 23.94 365.26 9.8 287 1015 1.2 300 9 1010 1212 1.5 10−5 3.3 10−2 9.8 10−2
Wm−2 degrees hours Earth days m s−2 J kg−1 K−1 hPa kg m−3 K kilometre J K−1 kg−1 J K−1 m−3 m2 s−1 m K−1 s−2 K m−1
we consider the influence of the low Martian air density for parameters of interest in boundary-layer meteorology, given this information about the velocity scale. The Reynolds number, Re = U /ν, is frequently used as a measure of the complexity and degree of turbulence in fluid dynamics. Here U is a characteristic velocity scale, and is a characteristic length scale of the problem considered. If we use U as 10 m s−1 , and let be the atmospheric scale height of 10 km, Re is seen to be 108 and 1010 for Mars and Earth respectively. For a large wind tunnel on Earth we can use the same U and an value of 1 m to obtain a Re of about 106 . Hence, it is seen that the Reynolds number for the Martian atmosphere lies between the Reynolds number for the Earth atmosphere and for a larger wind tunnel. While the reduced Re for the tunnel relative to the atmosphere is due to the smaller scales of production, the reduction of the Martian Re is due to a larger value of the dissipation scale. This argument can be underlined by considering the Kolmogorov scale of viscous dissipation, η, given by η = (ν 3 / )1/4 ≈ (κzν 3 /u3∗ )1/4,
(1)
where we have used the near-ground approximation of turbulent dissipation, , as
≈ u3∗ /(κz), with u∗ being the friction velocity, z the measuring height and κ the
ASPECTS OF THE ATMOSPHERIC SURFACE LAYERS ON MARS AND EARTH
455
von Karman constant. Considering the measuring height for the Martian wind data, z = 1 m and a u∗ value of 0.5 m s−1 , we find η being about 0.3 mm on Earth, and 7 mm on Mars. Taking the customary scale for surface-layer shear production, κz, we find the range between the shear production scales and the dissipation scales to be κz = (κ(Rei ))3/4 , η
(2)
with Rei = uν∗ z , meaning that a Reynolds number, Rei , describes the scale range between shear production and dissipation. If we take our example from before, we find the ratio to be about 50 for Mars and 1250 for Earth. Therefore, we expect the inertial subrange of turbulence in the near surface atmosphere to be much less important on Mars than on Earth. Close to the surface the larger value of ν for Mars generally makes the surface conditions closer to smooth flow on Mars than over similar land surfaces on Earth. The conditions for rough and smooth flow are often formulated in terms of yet another Reynolds number, the roughness Reynolds number, Re0 = u∗ z0 /ν, where z0 is the surface roughness. The transition between rough and smooth flow is generally taken for a Re0 around 2–3 (Brutsaert, 1982). The value of Re0 is important for the difference between z0 and the corresponding value for the temperature field, z0T . Following Brutsaert (1982), Tillman et al. (1994) use z0T = z0 exp(−κX),
(3a)
with 1/4
X(Re0 , Pr) ≈ 7.3 Re0 Pr1/2.
(3b)
Finally we turn to the near-surface wind and temperature vertical profiles and the associated surface stress, τ , and sensible heat flux, H τ = −ρu2∗ ,
(4a)
H = −ρCp u∗ T∗ ,
(4b)
where T∗ is the surface scale temperature, defined by: T∗ = −w T /u∗ , with w T being the diabatic turbulent heat flux. Both on Mars and Earth the surface is heated by the sun during the day and cooled by longwave radiation during night. The energy balance at the surface can be written as Rn = H + LE + G, where Rn is the net radiation, LE the latent heatflux and G is the soil heat flux. On Mars Rn at the Viking and Pathfinder landing sites will typically be of the order of 50–70% of Rn at a similar dry desert like area on Earth (Savijärvi, 1999; Ye et al., 1990). Due to the low value of ρCp , the fluxes, H and LE , have little influence on the surface heat balance on Mars
456
S. E. LARSEN ET AL.
Figure 2. The strong regularity of the diurnal variations of the Martian atmospheric temperature as seen from Pathfinder measurements from the top and bottom thermocouples on the meteorological mast. Also shown is the temperature difference.
(less than about 2% according to Kieffer et al., 1976), while on Earth the turbulent sensible and latent heat flux can each easily exceed 50% of the net radiation at the surface. Hence, the Martian surface heat balance is almost exclusively a balance between the net radiation at the surface and the heat conduction in the soil surface layer. Given that Rn is of the same order of magnitude on the two planets, the absence of moderating atmospheric sensible and latent heat flux both by day and by night gives rise to a typically larger diurnal variation of surface air temperature on Mars. This is illustrated on Figure 2 showing the diurnal variation of temperature through several Sols from the Pathfinder site. Also apparent in the figure is the strong predictability of the Martian diurnal temperature signal, caused by the small influence of atmospheric distortion and variability. With the larger diurnal variation in surface temperature on Mars follows larger diabatic heat fluxes in the air as the near-surface atmosphere follows the surface temperature. Recalling that the wind speeds on Mars and Earth are of the same order of magnitude, see Figure 1, we expect that the larger heat flux will be reflected in larger T∗ values. The larger diabatic heat fluxes will as well tend to yield larger heights of the planetary boundary layer. In these arguments we have neglected the saturation and sublimation of CO2 and H2 O, which can maybe play a role for certain situations but are considered less important for the summer data at the Viking and Pathfinder lander sites (e.g., Savijarvi, 1999). Also we have neglected dust storm situations, which will certainly influence the radiation balance. Indeed, the sharp reduction in the diurnal temper-
ASPECTS OF THE ATMOSPHERIC SURFACE LAYERS ON MARS AND EARTH
457
ature variation, noticed in the Lander 1 data in Figure 1, at Sol 220 and 320, are associated with large dust storms (Tillman et al., 1999) – compare also the optical depth data.
3. Measurement at the Martian Meteorology Stations More detailed descriptions of the Viking and Pathfinder surface layer meteorology stations are found in many papers on the Viking and Pathfinder landings, e.g., Chamberlain et al. (1976), Tillman et al. (1994), Landberg et al. (1995) [the two last references will be combined to TLL (1994) in the following, since the one is an extension of the other], Science (1997) and Schofield et al. (1997). Here we shall summarise the following. The Viking mission, which included two Landers, Viking 1 (22◦ N 48◦ W) and Viking 2 (48◦ N 225◦ W), began operation on Mars on 20 July 1976 and 3 September 1976. From Lander 1 data were collected for 2245 Sols, while Lander 2 transmitted data for 1050 Sols. The Pathfinder landed on Mars at 19◦ N 33◦ W on 4 July 1997 and continued data transmission for 92 Sols. Generally the meteorological measurements were conducted closer to the surface than is normal in meteorological surface-layer field campaigns with maximum measuring heights being 1–2 m above the terrain. Also the effort to avoid flow distortion around the sensors necessarily has been given relatively lesser priority than what would be normal in field measurements on Earth. Horizontal wind speed was measured at one height, the top level, basically by hot-film anemometry, while temperature was measured by thermocouples. On the Viking Landers, temperature was measured at one level only, while Pathfinder had temperature measurements in three levels. For Viking, the hot-film instrument was a constant overheat instrument with an overheat of about 100 K. The hot-film sensor on the Pathfinder was of the constant current type with a maximum overheat of about 30 K (at zero wind speed), a feature that made data reduction extremely complicated (Seiff et al., op. cit.). The frequency resolution of the thermocouples was about 0.1 Hz, while the hotfilm sensors had a somewhat better frequency resolution, and best for the Viking wind speed sensor. Both Pathfinder and Viking employed schemes with faster and slower sampling; the highest sampling rate for surface meteorology data for the Viking Lander was 1.2 sec, while for Pathfinder it was 0.25 sec. For the Viking analysed data, the minimum run duration was 30 min, while a typical run length analysed for the fast data from Pathfinder so far has been slightly less than 15 min. The sampling rate of many of the Viking data was often 16 seconds or longer making the correction for aliazing important. The meteorology data from Viking Lander 2 and Pathfinder have been compared with scaling laws applicable for the atmospheric surface layer, as is reported in TLL (1994) and Seiff et al. (op. cit.). Clearly, the data allow for only limited comparison, given that turbulent fluxes were not directly measured and given that vertical gradi-
458
S. E. LARSEN ET AL.
ents were measured only for the Pathfinder temperature measurements. However, the scaling laws allow us to relate the mean values of the velocity and temperature fields and turbulence characteristics of the same fields to each other. This comparison has, for a number of data sets from the Martian meteorological stations, been performed by comparing the power spectra of wind speed and temperature to the analytical forms that are presented in the literature, using parameters derived from the mean values of temperature and wind speed. The power spectra were chosen as being the simplest form of turbulence statistics available that allowed for both evaluation of the turbulence intensity and the importance of different scales, while also taking the instrument response properly into account.
4. Aspects of the Atmospheric Surface Boundary Layer Following Monin–Obukhov similarity, wind speed and temperature profiles can be written: z z u∗ ln − ψ , (5) U (z) = κ z0 L z z T∗ ln , (6) − ψT θ − θ0 = κ z0T L where U (z) is the wind profile, θ(z) the profile of the potential temperature of the air; θ0 is the surface value of θ(z) at height z0T , von Karman’s constant, κ, is a universal constant of the order of 0.4. The ψ functions depend on the thermal stability, with (0) = 0, and L is the Obukhov stability length that describes the ratio between the dynamic and thermal forces in the boundary layer and is defined as L=
T u2∗ , κg T∗
(7)
where T is the temperature and g is acceleration due to gravity. Equations 5 through 7 constitute relations between the mean values, U (z) and θ(z), and the turbulence characteristics, u∗ and T∗ . The turbulence intensity and structure can be described by its spectral structure. The power spectrum is often derived as a function of the frequency, f [Hz], and presented as a function of a normalised frequency, n = f z/U , stability parameter, L, measuring height, z, and the height of the atmospheric boundary layer, h. Hence, u∗ z fz nSµ (n) z z f Sµ (f ) , , Re = ,n = , (8) = =F µ2∗ µ2∗ h L ν U
ASPECTS OF THE ATMOSPHERIC SURFACE LAYERS ON MARS AND EARTH
459
where µ is the parameter considered, here wind speed, u, or temperature, T , µ∗ is the associated turbulence scale and Re is the Reynolds number, and where we note that f S(f ) = nS(n) due to the transformation rules for power density spectra. For the measuring heights considered here the height of the boundary layer, h, normally is neglected for thermally stable and neutral conditions. For unstable conditions, h is included and may either be measured or inferred. Often a prognostic equation of the following type is used, dh F (h, L, u∗ , γ , g, T ) − wh = (1 + B + *R)−u∗ T∗ /γ , (9) dt where γ is the vertical temperature gradient outside the growing thermal boundary layer, and different levels of complexities have been included in F (·) by different authors; B reflects the entrained heat at the top of the boundary layer. In its simplest approximation, B ≈ 0.2. When the upstream temperature profile is known, Equation (9) has been shown to be very efficient in predicting the boundary-layer height (Batchvarova and Gryning, 1991). The vertical motion at the top of the mixed layer, wh , is caused by convergence or divergence of the large-scale flow field. For cases with subsidence (downward motion) it has been found to be of considerable importance (Gryning and Batchvarova, 1999). As a first-order approximation wh can be considered proportional to h and to the horizontal divergence/convergence of the mean wind. The factor *R reflects the flux divergence of both longwave and shortwave radiation across the boundary layer. It has been found to be important for the Martian boundary layer (Ye et al., 1990; Kieffer et al., 1976). As a first approximation these authors suggest the following approximation: *R = n(1+C1 d ), with n ≈ 0.6 and C1 ≈ 1.9; d is the emissivity of dust, ranging between 0 for a dustless boundary layer, and 1 for an atmosphere with optical depth = 0.32 (Kieffer et al., 1976). The spectral forms for the horizontal wind speed are taken from TLL (1994). For unstable conditions, these are, 0.5ni 105nru (1 − z/ h)2 h 2/3 f Su (f ) = + , (10) 5/3 u2∗ −L (1 + 33nru )5/3 (1 + 15z/ h)2/3 1 + ni with ni = f h/U ; nru = n/(1 + 15z/ h). As seen the spectrum consists of two bell-shapes, one with maximum frequency corresponding to the boundary-layer height and the other with a maximum that scales with the measuring height. The expression reflects that the turbulence in the surface layer can be expressed using two height scales, one proportional to the measuring height above the ground, z, and the other proportional to the boundary-layer height, h. There is no complete consensus about the latter constant of proportionality; it is mostly found equal to about one, though larger factors up to 15 are cited in the literature (e.g., Etling and Brown, 1993), often associated with transient conditions as e.g., cold air outbreaks. Furthermore, closer to the ground
460
S. E. LARSEN ET AL.
than about seven metres, it has been found that the boundary-layer spectral height scale is reduced due to the ground-induced pressure forces, according to (Højstrup et al., 1990): hspec ≈ h(1 − exp(−z/zl )), with zl ≈ 7 m. For stable conditions the spectral form looks as follows, 2/3 ϕ 79x f Su (f ) −6 z −2 ϕh n + = 4 × 10 , (11) 2 5/3 u∗ L (1 + 263x ) ϕm with x = n/ϕm. The first part of this spectrum is mostly associated with gravity waves and has been found to describe the low frequency part of the stable surface layer well, although it is less well established than the second turbulence part (Larsen et al., 1985). In (11) additional functions have appeared. For z/L > 0, the dissipation function, ϕ (z/L), is given by: ϕ (z/L) = (1 + 2.5(z/L)0.6 )3/2 , and the dimensionless shear functions are given by: φh = φm (z/L) = 1 + 5z/L. For completeness, for z/L < 0, φm (z/L) = (1 − 16z/L)−1/4 , φh (z/L) = (1 − 9z/L)−1/2 and ϕ (z/L) = 1 − z/L. Note that the ψ functions in Equations (5), (6) derive from the dimensionless ϕ functions for velocity and temperature respectively. Unfortunately the surface-layer temperature spectrum is available only as analytical forms for stable and neutral conditions. For unstable conditions, they clearly show the same behaviour as the velocity spectrum, being dependent on the two height scales, h and z. But the interest in developing analytical expressions has been less here. The spectral forms available in the literature for neutral/stable conditions are, 53.4n f Sθ (f ) = T∗2 (1 + 24n)5/3
(12)
for neutral conditions and n ≤ 0.15, 0.16(n/n0 ) f Sθ (f ) = 2 θ 1 + 0.16(n/n0 )5/3
(13)
for stable conditions with n0 ≈ z/L. The expressions are derived from the Kansas data and are due to Kaimal et al. (1972) and Kaimal (1973) respectively. Equation (12) is focused on near-neutral conditions and includes as well a form for n ≥ 0.15 that is not important here due to the response time of the Martian temperature sensors. Equation (13) describes the stable spectra, and it is normalised by the temperature variance rather than the scaling temperature, T∗ ; it was used in the Viking analysis, where the derivation of T∗ was fairly uncertain and indirect and the temperature signal was affected by low resolution and noise. Equation (12) was employed for the Pathfinder analysis, where T∗ could be derived straightforwardly from the profiles, and the nighttime temperature signals had better quality.
ASPECTS OF THE ATMOSPHERIC SURFACE LAYERS ON MARS AND EARTH
461
The inertial range implied by the −5/3 power in all the spectra is terminated by the dissipation range, characterised by the Kolmogorov scale, η, as defined in (1). From the definition of η one finds (TLL, 1994) the dissipation cut-off, nd , 1 nd = z/2π(10η) = 20π
ϕ (z/L) κ
1/4
zu∗ 3/4 , ν
(14)
where the factor 10 multiplying η reflects the fact that the high-frequency end of the inertial range typically occurs at scales about a decade larger than η. Letting z/L ≈ 0 and using the same example in connection with (1, 2), z = 1 m, u∗ = 0.5 m s−1 , we find nd ≈ 1. This reflects that there will be little inertial range in the spectra found on Mars at the height of 1 m, as already discussed in Section 2. For some of the Viking spectra in TLL (1994) Equation (14) was more important for the limitation of the modelled aliasing than the instrumental filter responses.
5. Aspects of Data Analysis Basically, the data analysis has proceeded similarly for the Viking data and the Pathfinder data (TLL, 1994; Seiff et al., op. cit.). Data were selected, preferably from wind directions with minimum flow distortion, see below, and mean speed and mean temperature(s) were computed. From the profile expressions in Equations (5) through (7) the values for u∗ , T∗ and z/L were estimated. After computation of the spectra from the turbulence data, the spectral results were compared to the relevant analytical models, given in Equations (10) through (13), with parameter values determined from the profile estimated values of U , u∗ , T∗ and z/L. The boundary-layer height, h, needed in connection with (10), was determined from a simplified version of (9) with B = 0.2, F (·) = h, wh = 0 and *R = 0: h
dh = 1.2(−u∗ T∗ )/γ . dt
Integration between sunrise, t0 and t yields, h(t) = γ
−1
t
1/2
2.4(−u∗ T∗ )dt + h (t0 ) 2
.
(15)
t0
In spite of its simplicity, the application of (15) worked well for the Viking data. Therefore, and also because lack of information made use of a more complete form of (9) unpromising, it was used for the Pathfinder data as well. The equation implies that the daytime boundary-layer height can be determined by integrating the heat flux from sunrise to the time of interest, provided that γ is determined. A lapse rate of 1.3 K−1 km was used, being somewhat smaller than the adiabatic lapse rate, 4.5 K−1 km, and even smaller that the strongly stable lapse rates prevailing close to the
462
S. E. LARSEN ET AL.
ground at night. The value of 1.3 K−1 km was estimated as a maximum value from the Viking 2 descent (Seiff and Kirk, 1976). However, the value of Seiff and Kirk is a late afternoon value and therefore can reflect the temperature conditions within the convective boundary layer, not the lapse rate outside this layer. An argument for the use of a small lapse rate is that the morning unstable boundary layer, after having grown through the stable layer just above the surface, will for the first kilometre or so grow through a residual layer left over from yesterday’s unstable daytime layer. This phenomenon is well known on Earth, see e.g., Figure 1.7 in Stull (1988). Such a layer can be almost isothermal, as was found by Seiff and Kirk (1976). The derivation of T∗ and u∗ was different for Viking and Pathfinder due to the difference in the data available. On the Viking stations wind and temperature were available at one height only. TLL (1994) followed a methodology applied by Sutton et al. (1978) – a surface temperature was derived from a thermal model. In a parameter study, z0 was allowed to vary between 3 and 30 mm. The surface temperature was associated with the height z0T determined from (3). The different analytical spectral forms corresponding to different z0 values in the parameter studies are reflected in the different curves in the Viking spectra in Figures 5 and 6. For the Pathfinder station three levels of temperature were available, hence T∗ could be derived directly from the profile, without the need for either a model derived surface temperature nor an estimate of z0T . Also at the Pathfinder station, wind speed and direction were measured at only one level. Therefore the u∗ values were derived similarly to the Viking analysis, using an estimated terrain roughness. The z0 value was derived from the images of the surroundings of the lander as reported in Plates 5, 8–10 in Science (1997), where the distributions of rocks around the Landers are described in such a way that one can apply the formula for roughness, firstly developed by Lettau (1969), z0 = 0.5H
HD , A
(16)
where H is the average height of the roughness elements, D their horizontal width (such that H D is the crosswind area), and A is the average surface area per rock (total area divided by number of rocks). From the above-mentioned plates in Science (1997) one finds from the overall rock distributions that D is between 0.08 and 0.2 m with 0.1 m as a central value, and H is between 0.075 and 0.09 m. Further, there is a total of 15–18 rocks m−2 . Through (18) this yields an average z0 value of about 10 mm. The derived value is supported by TLL (1994) who, by testing z0 values in the range from 3–30 mm, found z0 = 10 mm to yield the best roughness value for Viking Lander 2, which has a rock size distribution very similar to those around Pathfinder, as seen in the above mentioned plates in Science (1997). Finally, we turn to the issue of flow distortion. As seen from Figure 3, depicting the meteorological stations of the Viking and the Pathfinder Landers, it is necessary to consider the influence of flow distortion on the data. As is known, the wind speed
ASPECTS OF THE ATMOSPHERIC SURFACE LAYERS ON MARS AND EARTH
463
Figure 3. The left-side picture shows the Martian landscape as seen through the meteorological boom of the Viking Lander 1, about 1.6 m above the terrain. The right side picture shows the 1.1-m high meteorological mast of the Pathfinder Lander looking over a similar landscape.
measurements especially are fairly sensitive to flow distortion, while temperature measurements are less sensitive. The different models used for estimating the flow distortion are shown in Figure 4. For the Viking data, TLL (1994) modelled the Lander body as a sphere partly submerged in the ground, and the flow distortion was estimated both with respect to a relation between the free stream wind and the measured wind, and with respect to the free stream height of the trajectory passing through the sensor. The free stream height was then considered the ‘z’ to be used in the surface scaling laws described in Section 4. The importance of the correction change was evaluated by varying z between the measuring height of 1.6 m and the typical corrected free stream height of 0.9 m. The relative overspeeding of the sensor was found to be of the order of 15%, dependent on wind direction, see Figure 4. For the Pathfinder meteorological mast, Seiff et al. (op. cit.) use a linearized WAsP-flow model by Troen and Petersen (1989) to estimate the change in wind speed at the meteorological mast, induced by the Lander body and the nearest terrain features. Pathfinder was situated in a shallow ditch. The petals rode on the collapsed balloons at the top of a number of rocks, such that the petals, and thereby
464
S. E. LARSEN ET AL.
Figure 4. Flow distortion modelling for Viking and Pathfinder. Upper right-side figure: The Viking Lander as a sphere partly submerged in the ground. A trajectory passing directly through the sensor is indicated. Upper left-side figure shows the relative over-speeding, computed as potential flow. The direction of the direct trajectory is marked by • (TLL, 1994). Lower right-side figure shows elevation contours (0.1-m height differences) used to compute Pathfinder flow distortion at the position of the meteorological mast, indicated by an arrow, Seiff et al. (op. cit.). The lower left-side figure displays the relative over-speeding as estimated by the linearised flow model of the WAsP wind program (Troen and Petersen, 1989).
the zero level for the meteorological mast, is about 0.5 m above the soil surface, as depicted in the Figure 4. As seen the derived speed at the 1-m measuring height of the wind sensor is between 5 and 10% for the winds from around 0 and 200 degrees, the two characteristic wind directions in the data set considered. The correction on the temperature is considerably smaller and has been neglected. The turbulence structure of the flow reacts to the mean flow modifications in ways that depend on the scale of the turbulence relative to the scale of the obstructing structure. For turbulence eddies much smaller than the structure, the eddies rapidly reach an equilibrium with the new mean flow. Eddies with a time scale corresponding to the time it takes to pass the structure, undergo rapid distortion, modifying the energy in the different turbulence components. Finally, wind fluctuations associated with eddies much larger than the structure undergo the same changes as the mean flow (Emeis et al., 1995; Frank, 1996; Mann, 1999).
ASPECTS OF THE ATMOSPHERIC SURFACE LAYERS ON MARS AND EARTH
465
The spectra presented in both TLL (1994) and Seiff et al. (op. cit.) have an upper frequency limit for useful information between 0.1 and 0.5 Hz. Between 0.1 and 1 Hz the derived spectra reflect a mixture of the turbulence spectrum, the low pass filters of the instruments, noise and aliasing. The horizontal wavelength of the turbulence, λ, is given by, λ = U/f . For the data set analysed from both Viking and Pathfinder, with U between 1 and 10 m s−1 , the smallest wavelength of turbulence to be seen by the analysis is between of the order of the Lander or somewhat larger. Most of the wavelength range of the spectra are much larger than the scale of the Landers. Therefore the correction to the turbulence amplitude is of the same magnitude as the correction of the mean flow.
6. Presentation of Results In this section we present sample results of stable and unstable wind and temperature spectra; we refer to the original papers (TLL, 1994, and Seiff et al., op. cit.) for more details. Figure 5 shows wind speed spectra from the two measuring systems, while Figure 6 shows similar temperature spectra. The Viking spectra have here been re-plotted in the same format as the Pathfinder spectra. All spectra are normalised with their appropriate scale, u∗ or T∗ . As seen from (12, 13), the spectral models for temperature are functions of only the normalised frequency, n = f z/U ; hence the temperature spectra are plotted versus n. The frequency dependency of the wind models is more complicated (9, 11); therefore these spectra are simply plotted versus the frequency in Hz. In Figure 5A, we show a stable layer Viking spectrum; also shown is the model spectrum (12). The higher level of both measured and modelled spectra reflects the importance of aliasing. Upper and lower bounds on the modelled spectral data are shown reflecting different combinations of the roughness, z0 , and measuring height, either the free stream height or the actual measuring height, see text above. Similarly, the daytime Viking spectrum below in Figure 5B shows both aliasing effects and different model curves reflecting measuring height and roughness combinations. The figures on the right hand side derive from the Pathfinder measurements. They show little aliasing, but both spectra show sensor response with a half-power point between 0.1 and 0.5 Hz. In the stable Viking spectrum the low frequency (n−2 ) part of (11) is not included, although a low frequency peak in the spectral data is present. TLL (1994) conclude that from the Viking data the n−2 section of the stable wind spectrum is weaker than given by (11), and not always present. For the stable Pathfinder spectrum, Figure 5C, the full model spectrum is shown, although its presence is also not conclusive from the Pathfinder data (Seiff et al., op. cit.). In Figure 5D is shown an unstable Pathfinder spectrum taken at 0830 local time. The solid curve reflects the boundary-layer height, h ≈ 2.5 km, estimated directly from (15), while the broken curve that fits the data better is based on h ≈ 6.3 km. Of all the convective cases studied from the two data sets, this is
466
S. E. LARSEN ET AL.
Figure 5. Stable and unstable wind spectra from Viking and Pathfinder normalised by u2∗ and plotted versus frequency (Hz). (A) a stable layer Viking spectrum (basic model as well as data and modelled data). The higher level of both the data and the modelled data reflects the importance of aliasing. Upper and lower bounds on the modelled data are shown, reflecting different combinations of roughness and measuring height. Similarly in (B), the daytime Viking spectrum shows both aliasing effects and different model curves reflecting different measuring height and roughness combinations. The figures on the right side derive from the Pathfinder measurements. They show little aliasing, but a sensor response function with a half-power point between 0.1 and 0.5 Hz. The stable Pathfinder model spectrum shows the n−2 part as well. (D) shows an unstable Pathfinder spectrum; the solid model curve reflects a boundary-layer height, h ≈ 2.5 km, estimated from (15), while the broken curve is based on a larger, h ≈ 6.3 km.
the only one where the h estimate by (15) using a γ of 1.3 K−1 km, does not fit the data. The deviation indicates an even greater increase in the boundary-layer height than predicted by this rather small γ value. From the discussion of the equations for growths of the daytime boundary layer (9, 15), it is seen that many (here neglected) terms could be responsible for such a fast growth. In Figure 6 examples of temperature spectra are presented for stable conditions from Viking and from unstable and stable conditions from the Pathfinder data set. Unstable temperature spectra were not analysed in TLL (1994) due to the lack of models for unstable temperature spectra. The stable spectrum from the Viking data is shown in Figure 6A, with the spectral model based on (13), again with different choices of z0 and measuring heights. In the Pathfinder plots (Figures 6B, 6C), three spectra are seen, reflecting the three measuring heights for temperature. They are plotted as function of the normalised frequency n and are compared to the spectral form of (12). For both stable (Figure 6B) and unstable plots (Figure 6C) the spectral intensity from the three heights are seen to be similar. The sensor
ASPECTS OF THE ATMOSPHERIC SURFACE LAYERS ON MARS AND EARTH
467
Figure 6. Modelled and measured temperature spectra normalised by T∗2 and plotted versus the normalised frequency n = f z/U . The stable temperature spectrum from the Viking in (A) show modelled curves based on (13), with different choices of z0 and measuring heights. The modelled Pathfinder spectra are derived from (12). On the Pathfinder plots three spectra are seen, reflecting the three measuring heights. For both stable (B) and unstable plots (C) the spectral intensity from the three heights are seen to be similar. The half-power point of the sensor response ≈ 0.1 Hz, for these runs corresponding to n ≈ 0.01–0.03. For the unstable spectrum the data show higher intensity in the low frequency end, reflecting the fact that the spectral function really corresponds to neutral to stable conditions.
response function with half-power point around 0.1 Hz is noted. For these runs and heights the frequency 0.1 Hz corresponds to n ≈ 0.01–0.02. For the unstable spectrum the data show a higher intensity than the model in the low frequency end, reflecting the fact that the spectral function really corresponds to neutral to stable conditions. As commented in the text there is no consensus form of the unstable spectrum in surface layer, although there is consensus that they qualitatively will correspond to the unstable wind spectra with a peak corresponding to the height of the boundary layer. 7. Discussion We have summarised aspects of the current knowledge about how well atmospheric surface-layer turbulence and mean vertical gradients on Mars relate through the same scaling laws as used on Earth. With the power spectra for the measured turbulence we have found that the scaling laws largely apply on Mars as well. Also we have discussed the differences in surface-layer turbulence to be expected
468
S. E. LARSEN ET AL.
from the overall differences of the planets and their atmospheres. We have found that these differences mainly rise from the low density of the Martian atmosphere. They manifest themselves mainly in larger variations of T∗ , giving rise to larger daytime boundary-layer heights (which may rise to the height of the atmospheric scale height), and in a larger kinematic viscosity, giving rise to smaller Reynolds numbers and a larger Kolmogorov scale. The larger daytime height of the atmospheric boundary layer on Mars is supported by the unstable surface-layer spectra, through their dependency on the boundary-layer height. In the context of the power spectral functions used, it is interesting to consider that all the used spectral expressions basically are constructed from the inertial sub-range, properly scaled, with extensions to lower frequencies, with the low frequency part included to yield the best and simplest fit to the point clouds there. On Mars we find the data to fit this low frequency form despite the virtual absence of an inertial sub-range at the measuring heights used. Finally, one can consider that some of the deviations between the data and the analytical spectra forms are not necessarily related to conditions on Mars. The formulations are tested at a height of 1 m, for which they are rarely used on Earth, since such low heights would rarely be suitable for turbulence measurements on Earth. Actually many of the expressions in Section 4 might for the first time have been taken down to 1-m height in connection with these analyses of Martian data. We note that the use of Lettau’s formula (16) on the distributions of rocks around both Viking Lander 2 and the Pathfinder site yields the same z0 values as derived by TLL (1994). In this connection it would be interesting to analyse data from the Viking Lander 1 site, which had a markedly different rock distribution from the two other sites (Science, 1997). We have generally, with one exception, found that the simple formulation of the daytime boundary-layer height (15), applied in connection with the presented analyses, fit the data well. However, only a small number of temperature profile measurements throughout the lowest 10 km of the atmosphere are available, so additional research into the structure of the boundary layer on Mars will be useful as many uncertainties remain about the formulation for growth of the daytime Martian boundary layer. Finally, we wish to stress that here we have here focused rather narrowly on the characteristics of simple scaling laws for the atmospheric surface boundary layer. Therefore, many other processes of interest and excitement in the Martian boundary layer have been neglected here. For example situations of extreme thermal stability (with possible condensation processes), signatures of synoptic and mesoscale phenomena, diurnal variations of wind speed and direction, dust devils and the atmospheric uptake of dust, and the importance of the dust loading for the atmospheric processes. Some of these subjects are considered more thoroughly in the listed papers, while others are still awaiting better data or models.
ASPECTS OF THE ATMOSPHERIC SURFACE LAYERS ON MARS AND EARTH
469
Acknowledgement The authors wish to express their gratitude for the support from colleagues, notably from the wind group of the Pathfinder ASI/Met team, Al Seiff, Tim Schofield, Jim Murphy and John Mihailov and from Dave Crisp on the radiation budget and on the importance of dust. The input from the reviewers is greatly appreciated as well. Support from the Danish Research Agency Contract 9602457/9802921 is acknowledged.
References Batchvarova, E. and Gryning, S. E.: 1991, ‘Applied Model for the Growth of the Daytime Mixed Layer’, Boundary-Layer Meteorol. 56, 261–274. Brutsaert, W. H.: 1982, ‘Exchange Processes at the Earth-Atmosphere Interface’, in E. Plate (ed.), Engineering Meteorology, Elsevier pp. 319–369. Champerlain, T. E., Cole, H. L., Dutton, R. G., Green, G. C., and Tillman, J. E.: 1976, ‘Atmospheric Measurements on Mars – the Viking Meteorological Experiment’, Bull. Amer. Meteorol. Soc. 57, 1094–1099. Colburn, D. S., Pollack, J. B., and Haberle, R. M.: 1989, ‘Diurnal Variations in Optical Depth at Mars’, Icarus 79, 159–189. Emeis, S., Frank, H. P., and Friedler, F.: 1995, ‘Modification of Air Flow Over an Escarpment – Results from the Hjardemål Experiment’, Boundary-Layer Meteorol. 74, 161–161. Etling, D. and Brown, R. A.: 1993, ‘Roll Vortices in the Planetary Boundary Layer: A Review’, Boundary-Layer Meteorol. 65, 215–248. Frank, H.: 1996, ‘A Simple Spectral Model for the Modification of Turbulence in Flow Over Hills’, Boundary-Layer Meteorol. 79, 345–373. Golitsyn, G. S.: 1969, ‘Estimates of Boundary-Layer Parameters in the Atmospheres of Terrestrial Planets’, Izv., Atmospheric and Oceanic Physics 5(8), 775–781. Gryning, S.-E. and Batchvarova, E.: 1999, ‘Regional Heat Flux Over the NOPEX Area Estimated from the Evolution of the Mixed-Layer’, Agric. For. Meteorol. 98–99 , 159–167. Højstrup, J., Larsen, S. E., and Madsen, P. H.: 1990, ‘Power Spectra of Horizontal Wind Components in the Neutral Atmospheric Surface Layer’, in Ninth Symposium on Turbulence and Diffusion. Amer. Meteorol. Soc., Boston, Mass. 305–308. Kaimal, J. C.: 1973, ‘Turbulence Spectra, Length Scales and Structure Parameters in the Stable Surface Layer’, Boundary-Layer. Meteorol. 4, 289–309. Kaimal, J. C., Wyngaard, J. C., Izumi, Y., and Coté, O. R.: 1972, ‘Spectral Characteristics of Surface Layer Turbulence’, Quart. J. Roy. Meteorol. Soc. 98, 563–589. Kieffer, H. H., Christensen, P. R., Martin, T. Z., Miner, E. D., and Palluconi, F. D.: 1976, ‘Temperatures of the Martian Surface and Atmosphere: Viking Observation of Diurnal and Geometric Variations’, Science 194, 1306–1351. Larsen, S. E., Olesen, H. R., and Håjstrup, J.: 1985, ‘Parameterisation of the Low Frequency Part of the Spectra of Horizontal Velocity Components in the Stable Surface Boundary Layer’, in J. C. R. Hunt (ed.), Turbulence and diffusion in stable environments, Oxford University Press, pp. 181–204. Lettau, H.: 1969, ‘Note on Aerodynamic Roughness-Parameter Estimation on the Basis of Roughness-Element Distribution’, J. Appl. Meteorol. 8, 820–832. Mann, J.: 1999, ‘Modeling of the Spectral Velocity Tensor in Complex Terrain’, in Larsen, Larosse & Livesy (eds.), Wind Engineering into the 21st Century, Balkema, Rotterdam, pp. 257–264.
470
S. E. LARSEN ET AL.
Murphy, J. R., Conway, B., Leovy, C., and Tillman, J. E.: 1990, ‘Observations of Martian Surface Winds at the Viking Lander 1 Site’, J. Geophys. Res. 95, 14555–14576. Savijärvi, H.: 1999, ‘A Model Study of the Atmospheric Boundary Layer in the Mars Pathfinder Lander Condition’, Quart. J. Roy. Meteorol. Soc. 125, 438–493. Schofield, J. T., Barnes, J. R., Crisp, D., Haberle, R. M., Larsen, S., Magalhaes, J. A., Murphy, J. R., Seiff, A., Wilson, G.: 1997, ‘The Mars Pathfinder Atmospheric Structure Investigation/Meteorology (ASI/MET) Experiment’, Science 278, 1752–1758. Science:1997, ‘Mars Parthfinder-Images’, Science 278, 1734–1742. Seiff, A and Kirk, D. B.: 1976, ‘Structure of Mars’s Atmosphere Up to 100 Kilometres from the Entry Measurements of Viking 2’, Science 194, 1300–1303. Siili, T. and Tillman, J.: 2000, ‘Martian Atmosphere’, in E. Pellinen and P. Raudsepp (eds.), Towards Mars, Oy Raud Publishing, Helsinki, Finland, pp. 201–216. Stull, R. B.: 1988, An Introduction to Boundary-Layer Meteorology, Kluwer Academic Publishers, 670 pp. Sutton, J. L., Leovy, C. B., and Tillman, J. E.: 1978, ‘Diurnal Variations of the Martian Surface Layer Meteorological Parameters During the First 45 Sols of the Two Viking Lander Sites’, J. Atmos. Sci. 35, 2346–2355. TLL : 1994: Tillman, J. E., Landberg, L., and Larsen, S. E.: 1994, ‘The Boundary Layer of Mars: Fluxes, Ftability, Turbulence Fpectra and Growth of the Mixed Layer’, J. Atmos. Sci. 51, 1709– 1727. TLL: 1995: Landberg, L., Larsen, S. E., and Tillman, J. E.: 1995, The Boundary Layer of Mars: Fluxes, Stability, Turbulent Spectra and the Growth of the Mixed Layer, Risø-R-701(EN), 54 pp. Tillman, J. E., Harri, A.-M., and Larsen, S. E.: 1999, ‘Martian climate variability: Multi-Year, in-situ Observations and Requirements’, in The Fifth International Conference on Mars, July 18–23, Pasadena, CA (unpublished, copy available from the first author). Troen, I. and Lundtang Petersen, E.: 1989, European Wind Atlas, European Community Publication, Risø National Laboratory, Roskilde, Denmark, 656 pp. Ye, Z. Y., Segal, M., and Pielke, R. A.: 1990, ‘A Comparative Study of Daytime Thermally Induced Up-Slope Flow on Mars and Earth’, J. Atmos. Sci. 47, 612–628.
