Return periods in current and future climate
crossref（2022）
摘要
<p>The distribution functions for large rain events <em>X<sub>c</sub></em> in current climate is denoted <em>F</em>(<em>x</em>) = P{<em>X</em><sub>c</sub> ≤ <em>x</em>} and for large rain events <em>X<sub>f</sub></em> in a future climate <em>G</em>(<em>x</em>) = P{<em>X<sub>f</sub></em> ≤ <em>x</em>}. A climate factor <em>k</em> is introduced, and it is assumed that P{<em>X<sub>c</sub></em> ≤ <em>x</em>} = P{<em>X<sub>f</sub></em> ≤ <em>k</em> <em>x</em>} corresponding to <em>G</em>(<em>k</em> <em>x</em>) = <em>F</em>(<em>x</em>). If we further assume that the distribution functions <em>F</em> and <em>G</em> have exponential tails, the following simple transformation of the return period in current climate <em>T<sub>c</sub></em> to the corresponding return period in future climate <em>T<sub>f</sub></em> can be deduced</p><p><em>T<sub>f</sub></em> = <em>T<sub>c</sub></em><sup>1/</sup><em><sup>k</sup></em></p><p>Applying a first order analysis on this equation with <em>k</em> as independent variable leads to a relation between the uncertainties of <em>k</em> and <em>T<sub>f</sub></em>. In terms of the coefficient of variations we get</p><p>CV{<em>T<sub>f</sub></em>} ≈ 1/ ln<em>T<sub>c </sub></em>CV{<em>k</em>}</p><p>This equation reveals that even with moderate uncertainty in <em>k</em>, the uncertainty in <em>T<sub>f</sub></em> is notably increased.</p>
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