Cumulative equations for continuous time Chicago hyetograph method

ABSTRACT The Chicago method is a classical method based on IDF curves for obtaining design hyetographs which present rainfall rates as continuous functions of time, one valid for times before peak and another for after peak. The intensity peak of rainfall is arbitrarily positioned at time zero, the function before peak counting time reversely and the function after peak with time axis normally. The time duration of the hyetograph before peak is determined by multiplying the total duration by a displacement factor with value between zero and one. This technical note presents both equations for before and after peak with the same time axis (time zero at the beginning of hyetograph) to facilitate applications of the Chicago method. The equations presented show cumulated rainfall depths resulting from exact integrals over chronological time of the original Chicago method’s rainfall intensity equations. That is, at every instant of time from the beginning of the hyetograph one has the exact value of cumulated rainfall. Thus, by decumulation, the sequential rainfall hyetograph depths are obtained. There is an advantage in using these equations which are easily introduced in spreadsheets.

摘要 芝加哥雨型法（Chicago method）是一种基于强度-历时-频率（IDF）曲线的经典方法，用于生成设计降雨过程线（hyetograph）：此类雨型将降雨强度表示为时间的连续函数，分别适用于峰前与峰后两个时段。该方法将降雨强度峰值任意设定在时刻0处，峰前时段的函数采用逆向计时，峰后时段则采用常规正向计时。峰前雨型的持续时长由总持续时长乘以取值介于0至1之间的位移系数确定。本技术简报提供了统一时间轴（以降雨过程线起始时刻为时刻0）下的峰前与峰后时段计算公式，以方便芝加哥雨型法的推广应用。本文给出的计算公式由原始芝加哥雨型法的降雨强度公式沿时序时间精确积分得到，可直接输出累积降雨量。换言之，从降雨过程线起始时刻起的任一时刻，均可获取精确的累积降雨量数值。由此，通过逆累积运算即可得到时序化的逐时段降雨过程线深度。此类公式易于在电子表格软件中嵌入使用，具备显著应用优势。