The effective average solar flux incident to a level surface at top of the atmosphere is \(\underline{\hspace{1cm}}\).
Show Hint
- 124 W/m\(^2\)
- 242 W/m\(^2\)
- 89 W/m\(^2\)
- 342 W/m\(^2\)
The Correct Option is D
Solution and Explanation
Step 1: Define the Solar Constant.
The solar constant is the total solar radiation energy received from the sun per unit of time per unit of area on a theoretical surface perpendicular to the sun's rays and at a distance of one astronomical unit (AU). Its value is approximately 1361 W/m\(^2\).
Step 2: Understand the "effective average solar flux".
This term refers to the solar constant averaged over the entire spherical surface of the Earth. The Earth intercepts sunlight over its cross-sectional area (\(\pi R^2\)), but this energy is distributed over the planet's full surface area (\(4\pi R^2\)).
Step 3: Calculate the average flux. \[ \text{Average Flux} = \frac{\text{Solar Constant} \times \text{Cross-sectional Area}}{\text{Total Surface Area}} = \frac{1361 \times \pi R^2}{4\pi R^2} = \frac{1361}{4} \] \[ \text{Average Flux} \approx 340.25 \text{ W/m}^2 \]
Step 4: Compare with the options.
The calculated value is approximately 340 W/m\(^2\). The closest option is 342 W/m\(^2\), which is a commonly rounded and used value in climatology.
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