Name:___________________________________
ATMS 373
4 March 2015
INDIVIDUAL EXAM#01
Choose the single best multiple-choice, True/False answer. Each question is worth four
points. Project (21) is worth a total of 20 points. EXAM#01 is worth 100 total points.
(1) Write down the triad of components that contribute to a healthy science according to a
prominent meteorologist.
(i) theory
(ii) observations
(iii) modeling
Name the prominent meteorologist (last name): Doswell, LP#1, sl#11
(2) According to a prominent meteorologist, we as forecasters should strive to be like
thermostats rather than being like thermometers. Explain in your own words what this
prominent meteorologist is trying to say using this analogy.
A forecaster needs to analyze the weather situation independently of models and
make an adjustment of the model forecast based on his/her assessment of the current
weather conditions. LP#1, pg#14
(3) In order for a computer weather model forecast to provide good guidance, it needs to
have two items properly represented. List these two items below.
(i) model has an accurate representation of the atmosphere [accurate physics]
(ii) accurate initial conditions, LP#1, sl#17
(4) Which of the following is not a factor that has led to an improvement in numerical
guidance skill over the past 40 years?
(a) improved representation of small-scale processes in the models
(b) increased availability of data
(c) increased power of supercomputers
(d) improved representation of Amalatoidal thermospheric drag, LP#1, sl#20
(5) Who formulated a system for numerically integrating the primitive equations in the
early part of the 20th Century? Explain why his attempt of a numerical integration over a
small region of Europe was a dismal failure.
Lewis Fry Richardson formulated the system and it failed because his initial conditions
used to initialize his model were not in hydrostatic or gradient balance. The imbalances
resulted in large-amplitude gravity waves that swamped the meteorologically significant
pressure tendency [p. 2-3 of text]
1
Name:___________________________________
ATMS 373
4 March 2015
INDIVIDUAL EXAM#01
(6) The process of blending a background or first guess field with observations in order to
create initial conditions for the numerical weather model is known as:
data assimilation, LP#1, pg#22
(7)
[a]
[b]
[c]
[d]
The equation shown above is the: meridional momentum eqtn, see LP#2, sl#7
Name the terms:
[a] meridional acceleration
[b] advection
[c] horizontal pressure gradient force
[d] Coriolis force
(8) Which of the following filtering approximations does not eliminate acoustic waves?
(a) anelastic
(b) hydrostatic
(c) neutral stratification, LP#2, sl#29
(d) quasi-geostrophic
(9) Calculate below the backward difference approximation to
du
[in s-1] at x = 0 given
dx x
the conditions:
du
dx

x
u ( x)  u ( x  x)
, LP#2 board notes
x
(10) “Numerical results demonstrate that an approximate solution to an ordinary
differential equation can be found using finite differences and that, by using a smaller
time increment, the accuracy of the problem can be increased.” Explain the cost of using
a small time increment in terms of the constraints of operational weather forecasting.
A smaller time increments increases the number of computations per forecast hour p. 23-25 textbook
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Name:___________________________________
ATMS 373
4 March 2015
INDIVIDUAL EXAM#01
(11) The partial differential equation
 2u
 2u  2u
2

0
xz z 2
x 2
qualifies as (circle one):
a hyperbolic equation
a parabolic equation
an elliptic equation
LP#3, sl#27-28
(12) The Lax-Richtmyer theorem states; given a properly posed linear initial value
problem, and a finite difference scheme that satisfies the ______________ condition, then
the ____________ of the FDE is the necessary and sufficient condition for convergence.
consistency, stability, LP#3, sl#43
(13) List one advantage and one disadvantage of the centered-in-time (leapfrog) scheme
as applied to the linear one-dimensional advection equation.
Advantage: as long as the CFL criterion is met, scheme is neutrally stable (p. 49 of text)
Disadvantage: scheme has two amplification factors, two solutions  a computational
mode (p. 49-51)
(14) What is the CFL stability condition for the leapfrog, centered-in-space scheme of the
linear one-dimensional advection equation (in terms of ‘c’, ‘Δt’, and ‘Δx’)?
Abs(c*dt/dx) .le. 1 (p. 48 of text)
(15) Determine the largest allowable time step [seconds] for the linear one-dimensional
advection equation problem [using the leapfrog, centered-in-space scheme] that will
guarantee numerical stability given that the largest propagation speed of the weather of
interest is 20 m s-1 and the horizontal grid spacing is 20 km.
dt .le. abs[dx/c] = 20,000 m/20 m s-1 = 1,000 seconds
3
Name:___________________________________
ATMS 373
4 March 2015
INDIVIDUAL EXAM#01
(16) Development of cyclones due to ________________ cannot occur in a barotropic
Quasi-Geostrophic (QG) model.
baroclinic instability (LP#4, sl#6)
(17) List three mean properties that must be conserved in a barotropic QG model if our
numerical difference schemes have been properly implemented.
(i) mean vorticity
(ii) mean enstrophy
(iii) mean kinetic energy (p. 89 of text)
(18) If the phase speed of the waves does depend on the wave number, then waves of
different wave numbers will travel at ________ speeds and the signal shape ________
change with time.
(a) different, will, p. 120 of text
(b) different, will not
(c) equivalent, will
(d) equivalent, will not
(19) The Arakawa grid having the worst dispersion properties, no matter the stability of
the atmosphere in the linearized barotropic primitive equations model is ________.
(a) Grid A
(b) Grid B
(c) Grid C
(d) Grid D, see p. 133-136 of the text
(20) Summarize which Arakawa grids have the least stringent stability condition using
the following time-differencing schemes,
(i) leapfrog => A grid, p. 140 of text
(ii) Adams-Bashforth => C grid, p. 140 of text
as applied in the barotropic primitive equations model. Clarify below what is meant by
least stringent stability condition (is ‘least stringent stability condition’ a positive or
negative attribute?).
least stringent means this grid allows the largest dt, to maintain CFL stability, which is
advantageous since a smaller number of time steps (computations) is needed to complete
the time integration (numerical forecast).
4
Name:_____________________________________
Work to be included for Problem _____ of Exam _____ in class ATMS _____
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