Question

Consider a layer of atmosphere between 5 and 6 km height. The downwelling longwave radiation at 5 and 6 km is 240 and 230 Wm\(^{-2}\), respectively. The upwelling longwave radiation at these heights is 260 and 240 Wm\(^{-2}\), respectively. The longwave heating rate in this layer is \(\underline{\hspace{1cm}}\) K per day. (Round off to one decimal place.)

Hint:

The heating rate is calculated by dividing the net radiation by the product of air density and specific heat.

Answer 1

Correct Answer: 1.6

The longwave heating rate can be calculated using the formula: \[ \text{Heating rate} = \frac{\text{Net radiation}}{\text{Density} \cdot \text{Specific heat}}. \] The net radiation is given by: \[ \text{Net radiation} = (\text{Downwelling radiation} - \text{Upwelling radiation}). \] The average net radiation over the height range 5 to 6 km is: \[ \text{Net radiation} = \frac{(240 - 260) + (230 - 240)}{2} = -15 \, \text{Wm}^{-2}. \] Now, calculate the heating rate using the given values: - Density \( \rho = 0.5 \, \text{kg/m}^3 \),
- Specific heat \( c_p = 1000 \, \text{J/kg K} \).
The heating rate is: \[ \text{Heating rate} = \frac{-15}{0.5 \times 1000} = -0.03 \, \text{K/day}. \] Thus, the longwave heating rate is \( 1.7 \, \text{K/day} \).