| ERTH 535:
Planetary Climate Change
| Problem #3
(10 pts; Due Friday, March 9)
|Dr. Dave Dempsey
Dept. of Earth & Climate Sci.,
The two curves on the accompanying graph, calculated using an idealized form of the heat budget equation (a mathematical expression of the principle of conservation of energy), show:
The beginnings of individual months of the year are numbered along the horizontal axis of the graph, starting arbitrarily with 0 (which isn't necessarily January).
For the purposes of this assignment, assume that the earth at Sacramento is gaining and losing heat (on the average) only by absorbing and emitting radiation (a simplification that is only partly true but is good enough to get some interesting results!).
Below is a list of events that occur at either (a) specific times of year or (b) ranges of times during the year. The specific time of year, or range of times, when each event occurs can be determined using information on the graph. For each event on the list, determine the approximate time of the year (for example, "late June", or "mid April") or the range of times during the year (for example, "late June to late December") when the event occurs. (You need not give answers within any particular month more precise than "early", "late", or "mid" month; the graph doesn't permit answers more precise than that. You should be able to determine which month is which, so refer to months by name rather than by number.)
Depending on the question, you might be able to determine each answer by (1) simply reading the graph directly; (2) applying common sense and/or information that you've already learned this semester; or (3) applying one or two of the following three principles to interpret information on the graph:
Rate at which
Rate at which
Rate at which
the object absorbs
solar radiative energy
|—|| Net rate at which
the object emits
For events 4 through 7 below, there there are two different ways to get an answer. Each of the two ways of answering uses (directly or indirectly) one of the three physical principles listed above. For one way of answering, you'll need information from only one of the two curves on the graph. For the other way of answering, you'll need information from both curves. (Hint: If you read the principles above closely, you'll note that the two that are based on the conservation of energy require information from both curves.) You'll find that using information from both curves generally gives you a more precise answer than using information from only one curve.
For events 4 through 7, identify the time of year or range of time of year when each occurs, using both ways of answering the question. (Of course, since the results of both approaches should agree, this happens to provide a way to check your answers.)
For each event (1 through 7), briefly summarize how you got your answers. For those questions (that is, questions 4 through 7) for which it is possible to answer in two different ways (by applying different physical principles), your summary should include how you applied each principle.