Three Stages on How to Calculate Advection

In the first stage, I calculated temperature advection assuming that the positive x-direction is directly parallel to the wind flow.  Therefore, there is no vertical wind component.  Thus, I only had variable u from the wind speed, partial derivative with respect to temperature, and partial derivative with respect to horizontal distance.  I measured the wind speed, temperature, and distance based of a random location in central Michigan on September 11, 2014 at 1200 UTC from the 0000 UTC run from the GFS211, NAM40, and RUC2 models.  The wind speed had to be converted from knots to meters per second.  Then, the temperature difference was calculated from one isotherm to another isotherm in the positive x-direction.  Lastly, the distance was measured similar to the temperature difference.  Then, I calculated advection by plugging the numbers into -u(partial derivative with respect to T/partial derivative with respect to x) for each of the three models. 

Here were the results: 
GFS211: -3.404e-4 K/s
NAM40: -2.605e-4 K/s
RUC2: -5.281e-4 K/s

In the second stage, I calculated advection for each of the three models exclusively by hand.  I recorded the change in horizontal distance (delta x), the change in vertical distance (delta y), the wind speed (U), the temperature change (delta T), the latitude (Phi), and the change in height (delta z).  With the vertical geostrophic wind equal to 0, all I needed was to calculate the horizontal geostrophic wind times the temperature change over the area of the parallelogram. 

Here were the results:
GFS211: -3.338e-4 K/s
NAM40: -3.304e-4 K/s
RUC2: -6.658e-4 K/s

In the third stage, I plotted the advection on the weather maps via GEMPAK and NAWIPS.  Please see the maps below.  Temperature (K), wind speed (knots), heights (m), and advection (1e-5 K/s) were plotted at 850 mb.  The GFS and RAP models were very close to the values I calculated in stages 1 and 2.  Keep in mind that the advection values on the maps were in 1e-5 K/s instead of 1e-4 K/s that were calculated earlier.  However, the NAM model was off by a factor of 2 compared to my computed values. 







Then, based on my three different stages of calculating advection, I forecasted a four Kelvin temperature drop three hours after 1200 UTC 11 September 2014 at 850 mb for (43.18, -84.55).  It was actually a three Kelvin decrease.  Thus, the forecast was only one Kelvin cooler (280 K) from its actual measurement (281 K).  The rate of advection was key to making the forecast.  In one hour based on an advection rate of -3.5e-4 K/s, the temperature would decrease by 1.26 Kelvin.  Hence, it was a reliable forecast.
   
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