Chelsea: Advection Explanation

For the first stage I calculated advection using the equation given. -u is the wind speed, the partial derivative Temperature over partial derivative x which is the horizontal component. I then can let the partial derivatives become delta T over delta x by finite differences. We are able to figure out delta T by looking at the change in the isotherms on the NMAP2 plots for September 11, 2014 the 00Z run for the 12Z time. We use the plotting tool to get the change in x parallel to a point determined in Michigan. The first calculation assumes that there is no vertical wind. After plugging in the values for each component my calculations are as follows:
RUC2: -5.36E-4  K s^-1
GFS211: -2.99E-4 K s^-1
NAM40: -2.74E-4 K s^-1

For part two we need to manipulate the advection equation to include the coriolis parameter, gravity, the differences between the height contours, the differences between the two temperature isotherms and the area of intersection of the contours. So -u(delta T/ delta x) becomes U_g = (-1/f) [(g*deltaz)/delta x] (delta T/ delta x). We know that f = 2 (omega) sin(phi). Omega is the constant 7.292E-5 rad/sec and phi is the latitude of the point chosen in Michigan. Each of my calculations are as follows:

RUC2: -6.61E-4 K s^-1
GFS: -2.85E-4 K s^-1
NAM: -2.97E-4 K s^-1

As for part three I plotted advection on NMAP2 through NAWIPS and GEMPAK at 850 mb level. My values for the RAP and GFS were within the advection calculated within the models. My NAM calculations were not within the ranges that the model calculated. My plots are below:

The advection values that are were calculated on the models are between -2.4E-4 K s^-1 and -3.2E-4 K s^-1. Both of my calculated values for the GFS do fall within this range. 

The NAM range calculated by the model is between the values -3.2E-4 K s^-1 and -4.0E-4 K s^-1. My values do not fall within those values as shown above.

The range calculated by the models fall between -4.0E-4 K s^-1 and lower. Both of my calculated RAP values are colder so they do fall within the calculated range. 

RUC2- verified:
For my 3 hour forecast I assumed advection would adjust by multiplying the found advection by (3600 s/ 1 hr)*(3hr) so this would give me a new value of -5.79 K and for advection with the geostrophic winds I calculated a new value of -7.14 K. This is not equal to the RAP at 1500Z. The NMAP2 values were between -1.6E-4 to -2.4E-4.