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Antecedent moisture is a term that describes the relative wetness or dryness of a sewershed, which is a function of the distribution of recent rainfall, temperature, seasonal variations and other dynamics. Because of the complex transport mechanisms of these flow sources, they are heavily dependent on variables that are not normally included in runoff models such as soil moisture conditions and season effects. These variables continuously change during storms and in between storms in response to antecedent moisture. The figure below demonstrates the antecedent moisture effects for several storms that occurred in a five week period in Wayne County, Michigan. The figure shows the I/I flow (black line) after the diurnal sewage flow has been filtered from the signal. The period experienced nearly 8-inches of rainfall, which is over twice the average for this area. Note that the four storms circled in red all had similar rainfall volumes and patterns, and yet the system response increases for subsequent storms as the antecedent moisture conditions increase. This clearly demonstrates the impacts of antecedent moisture on sewer systems.
Typical runoff models are unable to account for these antecedent moisture conditions, because they require the pre-selection of a static design capture coefficient. The difficulty in using a static model is demonstrated in the figure below. The figure shows the results of a static runoff model calibrated to the first storm event. The model output is shown in red. Although the static model produces a good fit to the first storm, it is unable match subsequent storms as the system is wetted.
A new model has been developed by i3DLab called the Antecedent Moisture (AM) Model. The model was developed specifically to simulate the impacts of antecedent moisture on I/I. The i3D model incorporates nonlinear dynamics to account for short-term antecedent rainfall conditions and long-term seasonal variation in the wet weather response. Unlike runoff models for I/I or complex physically based models, the resulting system identification model for antecedent moisture is uniquely identified for each sewershed, is parsimonious in nature (containing relatively few modeling parameters) and predicts the amount of antecedent moisture within the sewershed as a continuous variation in the capture coefficient. (Click here or on the image below for a larger version) The i3D AM Model is an alternative to purely physical based modeling using a procedure known as system identification. The basis of this approach is to allow measured data (in this case flow, rainfall and temperature) to guide the modeling process. It does not assume that the model must adhere to a specific preconceived notion of the physical system, but rather arrives at a statistically relevant description based on the data alone. Accordingly, this procedure differs from purely black-box modeling since it returns a model that offers insight into the underlying mechanics of the system. This is contrary to existing methods, which unduly enforce a predetermined set of physical principles on the data that may or may not be present in the actual system. The typical model structure that results from the i3D AM model process is shown below. Note that the numeric structure and values of each block in the model is not predetermined, but rather is identified based on the content in system observations (meter data).
The application of the i3D AM model results in a model that accurately predicts the system response variation to antecedent moisture conditions. This is demonstrated in the figure below that depicts the output from the AM model in red. Note that a single model accurately predicts both the first storm that occurred on dry AM conditions and the largest response that occurred on wet AM conditions. The model predicts the variations in capture coefficients for the entire simulation with no additional input or adjustment by the user.
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