Thermosphere - Energy Input - Energy Budget

Energy Budget

The thermospheric temperature can be determined from density observations as well as from direct satellite measurements. The temperature vs. altitude z in Fig. 1 can be simulated by the so-called Bates profile

(1) T = T_∞ - (T_∞ - T_o) exp{-s (z - z_o)}

with T_∞ the exospheric temperature above about 400 km altitude, T_o = 355 K, and z_o = 120 km reference temperature and height, and s an empirical parameter depending on T_∞ and decreasing with T_∞. That formula is derived from a simple equation of heat conduction. One estimates a total heat input of q_o≃ 0.8 to 1.6 mW/m2 above z_o = 120 km altitude. In order to obtain equilibrium conditions, that heat input q_o above z_o is lost to the lower atmospheric regions by heat conduction.

The exospheric temperature T_∞ is a fair measurement of the solar XUV radiation. Since solar radio emission F at 10.7 cm wavelength is a good indicator of solar activity, on can apply the empirical formula for quiet magnetospheric conditions.

(2) T_∞ ≃ 500 + 3.4 F_o

with T_∞ in K, F_o in 10- 2 W m−2 Hz−1 (the Covington index) a value of F averaged over several solar cycles. The Covington index varies typically between 70 and 250 during a solar cycle, and never drops below about 50. Thus, T_∞ varies between about 740 and 1350 K. During very quiet magnetospheric conditions, the still continuously flowing magnetospheric energy input contributes by about 250 K to the residual temperature of 500 K in eq.(2). The rest of 250 K in eq.(2) can be attributed to atmospheric waves generated within the troposphere and dissipated within the lower thermosphere.