Wx 354 HW 9 Solutions

 1. N1 a,b

a. Numerically forecast assuming .

 Note: from problem, it is clear that = 600 s.

 Use Eq. 14.4:

 b. Yes, there is evidence that the solutions are diverging.  At t = 0, . At t = 10 min, so it appears to be increasing.  At  t = 20 min, however, , a decrease from t = 0.  So one sequence is increasing and the alternate one decreasing, therefore the solutions at these time steps are diverging.

2. From eq. 14.6, , the maximum time steps for the given wind speeds are

 a. U = 1 m/s     

b. U = 2 m/s     

c. U = 5 m/s     

d. U = 10 m/s     

e. U = 15 m/s     

f. U = 20 m/s     

g. U = 50 m/s     

h. U = 100 m/s    

As the winds speeds increase, the maximum allowable time-step decreases to prevent air parcels from advecting into a neighboring  grid-cell during that time step.

3. N3 Use eq. 14.7 but substituting pressure for height:

a. surface weather station:

b. ship observation:

c. Southern Hemisphere manual analysis:

Discussion: Observations with smaller errors, that is, those which are more accurate such as a conventional surface weather station, get more weight in the analysis than the first guess field; observations with greater expected error, like the Southern hemisphere manual analysis get less weight than the first guess field in the analysis.

4. N4

 
5. N5 Use the regression equation from the solved example on p. 324: 

 
a.

I used a spreadsheet to make the calculations: