Imagine a scenario in which Santa Cruz receives the 2nd largest amount of precipitation that it has in its 109 years of precipitation monitoring. What is the return period of this precipitation?

Question

BlackTom AI · Accepted Answer

In order to determine the return period for a given rank within a historical record, we consider the concept of an annual maximum (or annual precipitation) series and use the typical relation RP = (N + 1) / m, where N is the number of years of data and m is the rank (with m = 1 for the largest event, m = 2 for the second largest, etc.).

First option: 0.018 years. This is an absurdly small return period for the second largest event in a 109-year record, since even the largest events typically have return periods on the order of many years, not fractions of a year. This option can be dismissed as inconsistent with the standard RP = (N+1)/m framework.

Second option: 55 years. Using the formula with N = 109 and m = 2 (the second largest), RP = (109 + 1) / 2 = 110 / 2 = 55 years. This aligns exactly with the expected return period for the second largest observation in a 109-year dataset.

Third option: 1.8 years. Similar to the first option, this is far too short for the second-largest event over a 109-year span. A return period this small would imply an extremely frequent event, which is inconsistent with the notion of the second largest in a long record.

Fourth option: 54.5 years. This is close to 55 but not exactly the standard calculation for the second largest with 109 years of data. Depending on rounding conventions, some analyses might approximate, but the conventional, textbook calculation yields exactly 55 years for RP when m = 2 and N = 109.

Summarizing, the logic hinges on applying the (N+1)/m rule to rank 2 within 109 years, which gives 55 years as the return period for the second largest precipitation event in the record. The other options deviate either by being implausibly short, or by not matching the precise calculation for this setup.

Imagine a scenario in which Santa Cruz receives the 2nd largest amount of precipitation that it has in its 109 years of precipitation monitoring. What is the return period of this precipitation?单项选择题

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