臺灣現行降雨強度－延時－頻率（Intensity–Duration–Frequency, IDF）公式多以單一雨量測站為分析單元，並針對不同重現期分別率定 Horner 型公式參數。此方式雖可保留各測站降雨特性，但隨測站數量、重現期條件及資料更新需求增加，參數表規模亦隨之擴大，造成資料整理與工程查用之負擔。因此，本研究在保留水利署既有單站設計降雨成果之基礎上，探討 Horner 型 IDF 公式之參數重整與區域化簡化方式。
本研究以經濟部水利署民國 113 年《全臺雨量站降雨強度延時公式推導》成果為基準，並以地質流域分區作為區域化分析單元。方法上，本研究以60分鐘設計降雨強度作為基準延時強度，結合尺度型 IDF 架構與時間平移修正，建立單站尺度型與分區區域化兩種參數配置。前者用以檢驗 Horner 公式重整後之可行性，後者則將部分延時轉換參數設定為分區共享，以評估參數簡化後之推估表現。
研究結果顯示，以60分鐘設計降雨強度重整 Horner 公式後，單站尺度型公式可有效重現水利署逐站公式之主要降雨強度變化。進一步採用分區區域化配置後，雖相較單站尺度型公式略有誤差增加，但仍可維持合理推估表現，並使參數管理量較傳統 Horner 公式減少約62.15%。延時分析結果顯示，本研究公式於1小時以內之短延時條件下表現較穩定，適用於都市排水等以短延時降雨為主之工程應用；當延時超過1小時後，高分位誤差有放大情形，應用於長延時設計雨型、累積雨量或滯洪容量估算時仍需審慎檢核。

Intensity–Duration–Frequency (IDF) formulas in Taiwan are currently made for individual rain gauge stations, with a different set of Horner-type formula parameters for each station and return period. Although this method keeps the rainfall features of each station, the number of parameters grows quickly when there are more stations and return periods. This makes data management and engineering use more complicated. Therefore, based on the existing design rainfall results from the Water Resources Agency (WRA), this study changes the parameters of Horner-type IDF formulas and tests if stations in the same region can share parameters.
This study uses the Derivation of Rainfall Intensity–Duration Formulae for Rain Gauge Stations in Taiwan published by the WRA in 2024 as the basis for analysis and adopts geological watershed regions as the spatial units for regionalization. The proposed method uses the 60-minute design rainfall intensity as the reference value, combining a scaling-based IDF model with a time-shift parameter. Two parameter setups are developed: a station-specific scaling formula and a regionalized scaling formula. The station-specific formula checks if the Horner-type formula can be restructured effectively. The regionalized formula allows selected duration-related parameters to be shared within each region to reduce the overall number of parameters.
The results show that the station-specific scaling formula can effectively reproduce the design rainfall intensity from the original WRA formulas. Although regionalization slightly increases errors, the overall performance remains good. Furthermore, the regionalized setup reduces the number of managed parameters by about 62.15% compared with traditional Horner formulas. In terms of rainfall duration, the proposed formula works more consistently for durations within one hour, making it suitable for short-duration applications such as urban drainage design. For durations longer than one hour, errors are larger for extreme rainfalls. Therefore, applications involving long-duration design storms, cumulative rainfall estimation, or detention pond design still require careful verification.

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