__Task__

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) |

T_{f}
= T_{i
} + (DT)_{}advection |
(Equation 3) |

where T_{i }is the temperature
at, say, 21Z today and T_{f} is the forecast temperature
for 21Z tomorrow.

__What do you need?
__

- T
_{i }= 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__

- T
_{i }= 21 UTC Temperature today (2/7/01) = 54F. (From the meteogram on the Surface Analysis portion of the Forecasting Exercise section). - Ds = 100 miles distance on the streamline drawn on the 12 UTC forecast surface chart (shown below) from the Model Forecast portion of the Forecasting Exercise section.
- V = average wind speed along Ds (shown below) is 10 knots (okay to use 10 mph) (shown below)

__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 **1**** ^{o}F/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.

T_{f}
= T_{i
} + (DT)_{}advection = 54F - 1.2F = **52.8F**