Abstract Low impact development is to restore natural hydrology in the urban environment. Thus, hydrologic characterization and hydrologic restoration measurement are crucial to low impact development research. The present study uses runoff frequency spectrum to present years of daily runoff events for characterizing flow regime, and develops a method to quantify similarity between runoff frequency spectra for measuring hydrologic restoration. The method was applied to case study of rainwater harvesting of a roof across five climate patterns with annual precipitation from 465.1 to 1807.9 mm/y. 26–30 years of daily runoff data were obtained by continuous mass balance simulation at daily time step that considered stochastic end-use water demand/usage of tanks. For comparison, similarity of total runoff amounts ( S t ) and similarity of runoff frequency spectra ( S d ) between undeveloped and developed scenarios were computed to measure hydrologic restoration. Maximum S t = 1 was found to be always achievable and only attained by a single rainwater tank size. Maximum S d = 0.34–0.78, which could be achieved by a size range larger than that with S t = 1. Compared with natural condition, total cumulative frequencies of rainwater tank with maximum S d were declined by 59.2–84.3%. The proposed method solves the problem of quantitative comparison of runoff frequency spectra with different frequencies and lengths, which has advantages of: 1) quantifying the extent of hydrologic restoration at daily temporal resolution, 2) finding a trade-off between reduction of roof runoff intensity and maintenance of natural runoff frequency, and 3) supporting decision-making on strategies to restore natural flow regime in the urban environment as much as possible.

中文翻译：

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一种计算径流频谱相似度的低影响开发水文恢复方法

摘要 低影响开发是为了恢复城市环境中的自然水文。因此，水文特征和水文恢复测量对于低影响开发研究至关重要。本研究使用径流频谱来呈现多年的每日径流事件以表征流态，并开发了一种量化径流频谱之间相似性以测量水文恢复的方法。该方法应用于年降水量从 465.1 到 1807.9 mm/y 的五种气候模式的屋顶雨水收集案例研究。26-30 年的每日径流数据是通过每日时间步长的连续质量平衡模拟获得的，该模拟考虑了随机的最终用水需求/水箱的使用。为了比较，计算未开发和已开发场景之间总径流量 (S t ) 的相似性和径流频谱的相似性 ( S d ) 来衡量水文恢复。发现最大 S t = 1 总是可以实现的，并且只能通过单个雨水箱尺寸来实现。最大S d = 0.34-0.78，可以通过比S t = 1更大的尺寸范围来实现。与自然条件相比，具有最大S d 的雨水箱的总累积频率下降了59.2-84.3%。该方法解决了不同频率、不同长度径流频谱的定量比较问题，具有以下优点：1）以日时间分辨率量化水文恢复程度，