Concept Plan for Getting Answer to Question: how will temperature change at San Francisco due to temperature advection alone.
The governing equations tell us what we need to know. To find the forecast temperature, we use the expression that relates the initial temperature to the final temperature by the change in temperature due to advection.
The change in temperature due to advection is calculated from a map that shows temperature gradients and wind.
Here are the two expressions.
(Equation 1) Tf = Ti + (DT)advection
(Equation 2) (DT)advection = -V (DT/Ds) (Dt)
Need to Know
For Equation 1, Need to know Ti, and Delta T (from Equation 2)
For Equation 2, Need to know V, Delta t and (DT/Ds)
(a) Ti = 15oC
(b) V = 100 km /h
(c) Delta t = 1 h
(d) Delta s = 100 km
For Delta T/Delta s = [T2 – T1]/Delta s need to know (figure 1):
(e) T2 = 15oC
(f) T1 = 30oC
Put (b), (c), (d), (e) and (f) into equation (2) to obtain
(DT)advection = - (100 km /h)( [15 oC – 30 oC]/100 km)( 1 h)
(g) (DT)advection= +15 oC
Put (g) and (a) into equation (1)
Tf = Ti + (DT)advection
Tf = 15oC+15oC = 30oC
Here you examine the result and decide if it is physically realistic given the constraint of the problem. This one is easy. You already know that if the air parcel at A moved to San Francisco the person at San Franciso would notice that the temperature would go up to 30oC by looking at Figure 1.
If your answer was a temperature fall, or that some unrealistic forecast temperature would occur (like -40 or 154) then you know you messed up somewhere.