Homework Questions for Chapter 13 - Weather Forecasting

Consult Syllabus for Due Date

*Questions 1 and 2 will be turned in for a grade.*

*SHOW ALL WORK , CIRCLE THE
CORRECT ANSWER, PLEASE BE NEAT AND **STAPLE YOUR HOMEWORK**!*

*ALSO, PLEASE USE A SPREADSHEET
FOR ALL GRAPHS*

*Follow
the Problem solving steps discussed in class*

1. In class we discussed that cloud cover at night will increase the minimum temperature observed. Another important factor to consider is the height of the clouds when forecasting the minimum temperature. The following relationship shows how much radiation is emitted between the ground and cloud layer above.

*E*_{net} is the net radiation transferred between the
ground and clouds. Remember that both the ground and cloud layer are
emitting radiation. *E*_{net} represents the amount of
radiation emitted by the cloud layer minus the amount emitted by the ground. *T*_{cloud} is the
cloud temperature, and *T*_{ground} is the
temperature of the ground. s is the Stefan-Boltzman
Constant.

(a) If E_{net} is positive, will the ground warm or cool
with time?
Explain. If E_{net} is negative, will the ground warm or cool with
time? Explain.

(b) From the above equation, will you observe a higher minimum temperature with high clouds or low clouds present during the nighttime hours? Explain.

(c) Using data from the U.S Standard Atmosphere, if the net radiation lost by the
ground is 50 W m^{-2}, what is the ground temperature if:

1. low clouds at 2.0 km AGL are overhead

2. high clouds at 7 km AGL are overhead.

HINT: (s = 5.67 x 10^{-8} W
m^{-2} ēK^{-4})

Also make sure that your temperature values are in ēK, not ēC

2. The equations that govern the state of the atmosphere are fundamentally chaotic. Another words, the forecast that the equations produce are very sensitive to the model initial conditions. We can replicate this situation with the simple example of 2-D convection in a tank of water, where the bottom is heated. Due to the heating at the bottom of the tank, the warm water near the bottom will rise and the cooler water at the top of the tank will sink. The equations that govern this motion can be expressed as:

where *C* gives the circulation of the
fluid. Circulation is a measure of rotation in the fluid which
will be larger for more vigorous convection. *L*
represents the left-right temperature distribution and *M*
indicates the amount of vertical mixing. **All three of
these variables are dimensionless**. **s****,
b,**** and ****r****
are dimensionless constants** while *D**t*
is the time increment.

a. Let's focus on a forecast of the circulation, C. Using the above equations, create a time series plot of circulation of the fluid versus time from time = 0 to time = 10. Use the following initial conditions (at time = 0): C(0) = 13.0, L(0) = 8.1, and M(0) = 45. Values for the constants are: s = 10.0 b = 8/3, and r = 28. Use a time step (Dt) = 0.01.

b. Now, on the same plot, create another time series of circulation versus time for M(0) = 44.

c. Create a final time series of circulation on the same plot with M(0) = 46.

d. Out to approximately what time can you have some confidence in your forecast. Explain.

You do not need to turn in all the numbers generated to make the plots. Please turn in some discussion of how you solved the equations.

3. Climatology shows that the skies over Vancouver, Canada are cloudy 327 days a year. If you were to forecast cloudy skies for every day of the year, how accurate will your forecasts be? Do your forecasts show skill? Explain.

4. Suppose that is is presently warm and raining. A cold front will pass your area in three hours. Behind the front it is cold and snowing. Make a persistence forecast for your area 6 hours from now. Would you expect this forecast to be correct? Explain. Now, make a forecast for your area using the steady-state, or trend method.

5. Explain how the phrase "sensitive dependence on initial conditions" relates to the final outcome of a computer-based weather forecast.

6. Describe with the aid of a diagram the movement of low and mid-level clouds for:

- cold-air advection
- warm-air advection

7. If a wave cyclone became stationary and its intensity were to remain the same, what would the spatial distribution of the isallobars look like?

8. You are in Calgary, Canada, 100 km east of the Rockies. The current wind is from the north. Looking at a prog for tomorrow, you see that the wind will be from the west. Will tomorrow's temperature be warmer or cooler than today? Explain.

9. What type of weather would you expect if the 700 hPa relative humidity is 95% and the 1000-500 hPa thickness is 5000 meters?

EXTRA CREDIT: For a three-day consecutive period, make daily forecasts for the maximum and minimum temperatures. Also record the observed daily maximum and minimum temperatures. For days when you were more then 5 degrees off from either the maximum or minimum temperature, provide an explanation for the forecast error. For example, let's say that your forecast for the minimum temperature is 0 degrees F while the actual temperature was -15 degrees F. When making your forecast, it was thought that clouds would be present overnight, whereas, in reality, the skies cleared out allowing for strong radiational cooling and therefore, much colder temperatures.