Z cpH tRK J

The temperature lapse rate is defined as the negative of the vertical temperature gradient, d T /d z. If the vertical temperature profile follows an adiabat, then T ~ pR/cp and dT/dz = -RT/cpH; therefore, RT/cpH is the adiabatic lapse rate in log-p coordinates. The factor in parentheses on the left side of Eq. (9.2.33) is just the difference between the adiabatic and the actual lapse rate of the atmosphere. Examination of the observed temperature field indicates that the lapse rate is less than adiabatic so this factor is positive. For an upward moving parcel, the left side of Eq. (9.2.33) represents the rate at which the temperature would decrease due to adiabatic expansion, while for a downward moving parcel, this term represents the rate of increase in temperature due to adiabatic compression. These processes are sometimes called adiabatic cooling and heating. Equation (9.2.33) states that adiabatic heating or cooling due to vertical motion is balanced by the radiative relaxation of the temperature field. Thus, if we have sufficient information to calculate the radiative equilibrium temperature field and the radiative relaxation time, the temperature field retrieved from infrared measurements can be used to estimate the large-scale vertical velocity.

Calculation of Te requires a detailed treatment of the absorption of sunlight by carbon dioxide and atmospheric dust, the absorption of sunlight and the emission of infrared radiation by the surface, and the transfer of infrared radiation in the atmosphere as discussed in Section 9.1. However, the basic characteristics of Te can be estimated without resorting to a detailed calculation. In the absence of significant dust loading in the thin Martian atmosphere, the distribution of the diurnally integrated sunlight incident on the planetary surface essentially determines the latitude dependence of the diurnal mean radiative equilibrium temperature. For the equinox condition shown in Fig. 9.2.1, we would expect maximum radiative equilibrium temperatures at low latitudes with a monotonic decrease towards either pole. We find that the observed temperatures indeed follow this behavior at the lower atmospheric levels; however, at pressures less than ~0.5 mbar, temperatures increase with latitude in both hemispheres from the equator up to high latitudes. We conclude that the thermal structure has been significantly perturbed away from the radiative equilibrium configuration by atmospheric circulation. If the observed temperature results from the zonal mean meridional circulation, then reference to Eq. (9.2.33) suggests that rising motion must occur at low latitudes resulting in adiabatic cooling at upper levels while descending motion at high latitudes results in adiabatic heating in both hemispheres. From considerations of mass continuity we infer that there must be a meridional flow aloft from low to high latitudes in both hemispheres with a return flow at low levels. With this relatively simple approach we have been able to qualitatively deduce the properties of the postulated meridional circulation. More sophisticated approaches have been taken using general circulation models to calculate the wind and temperature fields, and the latter are compared with the observations (Pollack et al., 1981; Haberle et al., 1982, 1993; Hourdin et al., 1993; Wilson & Hamilton, 1996).

LOCAL TIME (HRS)

Fig. 9.2.3 Martian atmospheric temperature as a function of local time and latitude for the 2 mbar level. These results were obtained by inversion of spectral measurements acquired with the Michelson interferometer (IRIS) carried on Mariner 9. A strong global dust storm was in progress, resulting in the observed large diurnal amplitude (Hanel et al., 1972a).

LOCAL TIME (HRS)

Fig. 9.2.3 Martian atmospheric temperature as a function of local time and latitude for the 2 mbar level. These results were obtained by inversion of spectral measurements acquired with the Michelson interferometer (IRIS) carried on Mariner 9. A strong global dust storm was in progress, resulting in the observed large diurnal amplitude (Hanel et al., 1972a).

We now turn to the second example of the study of a Martian dynamical phenomenon using remotely sensed infrared data. Thermally driven atmospheric tides form a significant component of the Martian meteorology, especially during global dust storms when a substantial amount of solar energy is deposited in the atmosphere due to absorption by the dust. At the time Mariner 9 was injected into orbit around Mars in 1971, a planet-wide dust storm was in progress, and the derived atmospheric thermal structure displayed a strong diurnal variation. Figure 9.2.3 shows temperatures in a layer centered at 2 mbar as a function of latitude and local time. An 'hour' in this case is defined as one twenty-fourth of a Martian solar day. A diurnal temperature fluctuation is observed at all latitudes, reaching a maximum of -30 K at 60° S.

Because the time scale of the anticipated atmospheric motion associated with the temperature fluctuations is only one day, the thermal wind approximation cannot be used. However, diurnal variations in the pressure and wind fields can be estimated from the observed temperature field using classical tidal theory. The basic concept of the formulation is sketched here; a detailed treatment can be found in Chapman & Lindzen (1970). The theory is based on a linearization of the primative equations. A motionless atmospheric reference state is assumed with temperature profile To(z) and a corresponding geopotential surface $0(z). It is further assumed that the diabatic heating and all other quantities vary as exp[i(s 0 — Mt)] where s is a longitudinal wavenumber and m is 2n/(solar day) or integer multiples thereof. The amplitudes of the time-varying, dependent variables are taken to be sufficiently small so that only terms of first order need be retained. With these assumptions,

a cos O

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Solar Panel Basics

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