Dust Distribution Scenarios in the MCD

This section outlines the dust distribution scenarios used for the GCM integrations which make up the Mars Climate Database. For the detailed rationale behind these choices, summaries of observational evidence and more references see Forget et al. (1999) and Lewis et al. (1999).

For all the scenarios, the vertical distribution of dust was calculated according to the formula,  

$$\frac{Q}{Q_0} = \exp\left(0.007\left(1 - {\rm max}\left[ \le... ...^{\left(70{\rm km}/z_{\rm max}\right)}, 1\right] \right)\right)$$ (2)

with p the pressure, p₀ a standard pressure (700Pa), Q and Q₀ the dust mixing ratio at the pressure levels p and p₀, and $z_{\rm max}$ the altitude of the top of the dust layer (where the dust mixing ratio is one thousandth of its value at p₀). This formula gives a rapid decay up to the height of the top of the dust layer and almost homogeneous dust mixing in the lower regions of the atmosphere. The function is illustrated for several different values of $z_{\rm max}$ in Figure 3.

In fact, Equation 2 was developed from a slightly simpler form in common use for Mars modelling, namely,  

$$\frac{Q}{Q_0} = \exp\left(\nu\left(1-\left(\frac{p_0}{p}\right)\right)\right)$$ (3)

where $\nu$ is now a parameter which determines the dust cut-off. This function is illustrated in Figure 4. Equation 3 matches Equation 2 when $z_{\rm max}=70$km and $\nu = 0.007$, which were roughly the conditions under which Equation 3 was derived to model the distribution of dust at the time of the IRIS observations from Mariner 9. The reason for modifying the formula to the form in Equation 2 was that it gives much more desirable properties in terms of the total dust contained below the cut-off threshold (with a broader region of homogeneity) and the vertical gradient of the dust is not so steep near the surface, especially when the dust is mostly low in the atmosphere, compare Figure 3 with Figure 4 when $z_{\rm max}=20$km and $\nu=1.0$. While having these desirable properties the function still matches the limited available observations when the dust is high in the atmosphere.

Baseline multi-annual model integrations were carried out for the database under two main scenarios: (a) seasonally-varying dust as observed during the Viking Lander years, but with the large dust storms removed; and (b) low uniform dust, perhaps appropriate to more recent observations of a clearer, colder Mars. In addition, scenarios were conducted for several seasons with much higher dust loadings, appropriate to dust storm conditions. The details of the scenarios follow.

• vik The standard Viking scenario with data provided for all twelve seasons from multiannual experiments. The total dust optical depth for the Viking case varied as a function of time to fit the Viking observations with peaks representing dust storms removed,  

  $$\tau(L_S) = 0.7 + 0.3\cos(L_S + 80^\circ)$$ (4)

  where $\tau$ is the optical depth and L_S the Solar longitude of Mars. The optical depth was uniform in the horizontal for the Viking baseline run. However, the cut-off of the dust in the vertical varied as a function of both time and latitude,  

  $$z_{\rm max}(L_S, \phi) = \left(60 + 18\sin(L_S - 158^\circ) - 22\sin^2\phi \right){\rm km}$$ (5)

  where $\phi$ is the latitude. $z_{\rm max}$ varies between 78km at the equator during the dusty seasons and 20km at the pole during the clear seasons.
• low The low dust scenario with data provided for all twelve seasons from multiannual experiments. The low dust case was conducted with a dust distribution which was invariant in latitude, longitude and time, with an optical depth of $\tau=0.1$ and a cut-off at $z_{\rm max}=30$km altitude.
• ds2 A dust storm with maximum optical depth 2. Data from these runs are only provided for the seasons when dust storms are most likely to occur; seasons 8, 9 and 10. The dust optical depth was set to double that in the Viking scenario, Equation 4, and the vertical cut-off for the dust was modelled as in the Viking scenario, Equation 5.
• ds5 A dust storm with maximum optical depth 5. Data from these runs are only provided for the seasons when dust storms are most likely to occur; seasons 8, 9 and 10. The dust optical depth was set to five times that in the Viking scenario, Equation 4, and the vertical cut-off for the dust was modelled as in the Viking scenario, Equation 5.

  

Figure 3: The variation of dust mixing ratio with height for different values of $z_{\rm max}$ according to the formula (Equation 2) used to compile the Mars Climate Database.

  

Figure 4: The variation of dust mixing ratio with height according to a formula (Equation 3) previously used in many Mars GCMs, with the $\nu$ parameter adjusted to give dust cut-offs at different heights. This function matches that in Figure 3 when $z_{\rm max}=70$km and $\nu = 0.007$.