On Modeling and Implications of Frequency-Dependent Phenomona in Drainage System Design

William James


This study is a simplistic numerical exploration of the frequency response of simple drainage elements, and likely falls outside existing professional desiderata.

Modern engineering analyses of drainage systems are performed exclusively in the time domain (TD, input and response functions are conceptualised as time series) – prognostic TD models are widely used for planning, design and operation, while diagnostic TD models are used for maintenance and litigation. These situations cover approximately 100% of our applications.

However multicellular storm systems that track with sensible speed and direction across complex drainage systems do occur routinely, particularly in summer convective storms in continental climates; common frequencies for such hydrologic input functions include thunderstorm cells of about two per hour or about 0.0005Hz; at significant storm speeds the resolved frequency might be finer, e.g. 0.002Hz (6/h) ; in slow-moving storms, perhaps 0.0001Hz (1 in 3h, 0.3/h). Effective speeds may be even slower in maritime climates.

Drainage system response to such input has the well-known character of engineering systems: in particular, frequency-dependent amplification (resonance) or cancellation (detuning), depending on the geometrical layout of the physical drainage system and its components. In other words, at the extremes hydrologic response may be either damped or amplified by both (a) attenuation devices (such as ponds and LIDs) and (b) tuning devices (such as pavement, diversion structures and interceptors).

Basically, the problem boils down to this: common design storm methods simplify complex storms in the original record into simplistic, single, causative input functions, and therefore cannot replicate frequency-dependent flood responses (which are watershed specific, obviously). Engineers thereby, typically, opt to ignore such effects in their designs (perhaps reasonably).

But such engineering system responses are readily demonstrated by realistic and simplistic PCSWMM models, and the results can be presented in both the time and frequency domains. In this study, storm hyetographs are generated as a sinusoidal wave train covering a spectrum of discrete, representative frequencies, and applied to an elementary SWMM drainage model. Computed responses are presented in both the frequency and time domains. Standard design storms are also applied and discussed.

Several implications arise which may be potentially serious: for complex weather systems, standard engineering design of drainage may inadvertently underestimate floods and expose designers and modellers to legal risks. Suggestions are made and a fast routine demonstrated in PCSWMM for modeling some frequency-domain effects and for evaluating such risks. Whether this is a real problem is still too early to say.

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