Calculating the Forecast Temperature Advection: An Example

Compute the temperature at Oakland at 21 UTC tomorrow (2/8/01) assuming that all the temperature change, if any, will be due to advection.

Governing Equations

 (DT/Dt)advection = -V (DT/Ds) (Equation 1)

where DT/Dt is the rate of temperature change (in units of o time-1) due to advection across the time interval considered.

 (DT)advection = -V (DT/Ds) (Dt) (Equation 2)

 Tf = Ti + (DT)advection (Equation 3)

where Ti is the temperature at, say, 21Z today and Tf is the forecast temperature for 21Z tomorrow.

What do you need?

• Ti = 21 UTC Temperature today (2/7/01)
• Ds = 100 miles distance along a streamline whose arrowhead is at Oakland and
whose tail is 100 miles upwind at 12 UTC tomorrow.
• V = average wind speed along Ds at 12 UTC tomorrow.
• (DT/Ds) = temperature gradient evaluated along the portion of the streamline indicated by Ds.
• (Dt) = total time interval over which the advection is expected to contribute to the forecast temperature (in this case, 24 hours)

Assumptions

• that the instantaneous temperature advection observed at 12 UTC tomorrow would occur across the whole forecast time interval
• that the temperature field depicted on surface charts is drawn at a constant elevation

Givens

Procedure and Calculations

1. Calculate the rate of temperature change due to advection.

Step 1: calculate the (DT/Ds) = temperature gradient evaluated along the portion of the streamline indicated by Ds (shown below). The procedure was shown on the Temperature Advection Assignment sheet. It is summarized on the chart below and, in this case ,is 1oF/100 miles.

Step 2: Substitute the values for the temperature gradient obtained in the last step and the wind speed (from the givens) into Equation (1) above to obtain the temperature advection.

-V (DT/Ds) = - ( 5 miles/hr) ( 1F/100 miles) = -5.0 X 10 -2 o hr-1

Step 3: Substitute the value for the temperature advection into Equation (2) and multiply by the time interval of 24 hours to obtain the 24 hour temperature change due to advection.

(DT)advection = -V (DT/Ds) (Dt) = (-5.0 X 10 -2 o hr-1) X 24 hr = - 1.2 F

2. Calculate the Forecast Temperature

Substute the value for the temperature advection just calculated and the 21 UTC temperature today (in this case, 2/7/01) into equation (3) to obtain the temperature forecast for 21 UTC on 1/8/01.

Tf = Ti + (DT)advection = 54F - 1.2F = 52.8F