To calculate the horizontal temperature advection by hand, I reoriented the x-y axes so the positive x axis is along the direction of the wind, this allows for the V component of the wind to be zero and the U component to simply be the wind speed. This simplifies the horizontal advection expression to -U(change in T)/(change in X) when using a finite difference approximation. I used this equation for the GFS211, NAM40 and the RUC2.
To calculate the advection by the geostrophic wind by hand, the same approach of reorienting the axes to cancel the V component was used. From there, a parallelogram whose sides consist of two isotherms and two 850mb heights was made and its area was computed using the distance tool. After deriving a formula for the geostrophic temperature advection, I determined a latitude for a point within central Michigan to measure the strength of the Coriolis Force and plugged in my known values to solve for the advection. This equation was used for the GFS211, NAME40 and the RUC2.
After computing both of the aforementioned advection terms, I then used NMAP2 to compute the horizontal temperature advection by using a restore file to set values for the scales, variables, units and overall display of the map. To determine NMAP2 values for temperature advection, I used the color scale off the the left of the chart to approximate the values for temperature advection.
Using the hand calculations and the values given by NMAP2 for temperature advection, I made a 3-hour forecast for the temperature change over central Michigan (from 1200 UTC to 1500 UTC). Specifically, I used the values from the NAM40 and the RUC2 since they represent the range for the temperature advection (both the lowest and the highest values). I compared my forecast to the actual values using the current RUC2 run at 1500 UTC. Values as well as a comparison can be seen below.