I guess I'm missing something here...but I've approached this question in every possible angle and im just not getting it! Could somebody point me in the right direction? Here is the question:
If the measured net radiation (Q*) for the lawn of your home in August is 700 W/m^2 and a typical Bowen ratio is 0.5, how much of this energy is being transferred to the atmosphere as heat and how much is being transferred in the form of evaporating water? Assume energy that is going into the ground is negligible Q(G) = 0.
Surface energy balance is: Q* = Q(H) + Q(E) + Q(G)
Bowen ratio = Q(H)/Q(E)
To solve this question, we need to use the surface energy balance equation and the Bowen ratio. Here's how you can approach it step by step:
1. Understand the variables:
- Q*: Measured net radiation (incoming and outgoing energy) in W/m^2.
- Q(H): Energy transferred to the atmosphere as sensible heat (heat that warms the air) in W/m^2.
- Q(E): Energy transferred as latent heat through evaporation of water in W/m^2.
- Q(G): Energy transferred into the ground (negligible for this question, so Q(G) = 0).
2. Plug the given values into the surface energy balance equation:
Q* = Q(H) + Q(E) + Q(G)
Since Q(G) = 0, the equation simplifies to:
Q* = Q(H) + Q(E)
3. Use the definition of the Bowen ratio:
Bowen ratio = Q(H) / Q(E)
Given that the typical Bowen ratio is 0.5, we can rewrite Q(H) in terms of Q(E):
Q(H) = 0.5 * Q(E)
4. Substitute the expression for Q(H) into the simplified energy balance equation:
Q* = 0.5 * Q(E) + Q(E)
Now we have an equation with a single unknown variable, Q(E).
5. Solve the equation for Q(E):
Combine like terms to simplify the equation:
Q* = 1.5 * Q(E)
Divide both sides of the equation by 1.5 to isolate Q(E):
Q(E) = Q* / 1.5
6. Calculate Q(E) using the given value for Q*:
Q(E) = 700 W/m^2 / 1.5
Q(E) = 466.67 W/m^2
So, approximately 466.67 W/m^2 of energy is being transferred in the form of evaporating water.
7. Calculate Q(H) using the obtained value for Q(E):
Q(H) = 0.5 * Q(E)
Q(H) = 0.5 * 466.67 W/m^2
Q(H) = 233.33 W/m^2
Therefore, approximately 233.33 W/m^2 of energy is being transferred to the atmosphere as sensible heat.
By following these steps, you should be able to determine the amount of energy transferred as heat and through the evaporation of water.