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Hydrologic model i3d white paper

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  • 1. 1010101001010101010101010010101 1010101010101010101010010101101 011100101010101010101010101100 i3D 010101010100101010101100 010101 A Technical Overview of the i3D Antecedent Moisture Model 1001010101010101010010101010101 101010101010101001010110100111 Antecedent moisture is a term that describes the relative wetness or dryness of a sewershed, 010101010101010101010110010101 www.i3dlab.com which is a function of the distribution of recent rainfall, temperature, seasonal variations and other 1010100101010101100 0101010100 The Antecedent dynamics. Because of the complex transport mechanisms of these flow sources, they are heavily 01010101010101001010101010101 Moisture Model (AMM) dependent on variables that are not normally included in runoff models such as soil moisture 10101010101010010101101001110 Calibrated using conditions and season effects. These variables continuously change during storms and in between 10101010101010101010110010101 flow metering data storms in response to antecedent moisture. 1010100101010101100 0101010100 and validated with 01010101010101001010101010101 an independent data set. The figure below demonstrates the antecedent moisture effects for several storms that occurred 10101010101010010101101001110 Automatically in a five week period in Wayne County, Michigan. The figure shows the I/I flow (black line) after the 10101010101010101010110010101 generates diurnal sewage flow has been filtered from the signal. The period experienced nearly 8-inches of 1010100101010101100 predictions without 0101010100 further data rainfall, which is over twice the average for this area. Note that the four storms circled in red all had 01010101010101001010101010101 manipulation. similar rainfall volumes and patterns, and yet the system response increases for subsequent storms as 10101010101010010101101001110 the antecedent moisture conditions increase. This clearly demonstrates the impacts of antecedent 10101010101010101010110010101 I/I Flow from M2 in Garden City moisture on sewer systems. 1010100101010101100 25 0.0 1010101001010101010 0101001010101010101 20 TypicAl AnTeceDenT 0.2 1.16" 1010101010101001010 MOisTure effecTs Rain (inches per hour) Increasing peak flows from similar rainfalls is the result of increasing 1.60" Observed I/I 1010011100101010101 I/I Flow (cfs) antecedent moisture conditions 15 0.4 1010101010110010101 Typical runoff models are unable to Rain 1010100101010101100 10 account for these antecedent moisture 1.49" 0.62" 0.6 1.45" conditions, because they require the pre- 0.16" 10101010010101010 0.41" selection of a static capture coefficient. 5 0.8 01010100101010101 10101010101010101 0 The difficulty in using a static model is 1.0 0101011010011100 9/10/2001 9/17/2001 9/24/2001 shown in the figure below for a static 10/1/2001 10/8/2001 Date 10/15/2001 10/22/2001 10/29/2001 0101010101010101010110010101 model calibrated to the first storm event. Although the static model produces a good fit to the first 1010100101010101100storm, it is unable match subsequent storms as the system becomes wetter. 0101010100 01010101010101001010101010101 10101010101010010101101001110 10101010101010101010110010101 has been developed A new model sTATic runOff MODel fiT 1010100101010101100called the i3D Antecedent Moisture 0101010100 Static Model Results from M2 in Garden City 25 0.0 01010101010101001010101010101Model. Unlike runoff models for 10101010101010010101101001110I/I or complex physically based 20 1.16" 0.2 10101010101010101010110010101 model for antecedent models, i3D Rain (inches per hour) Observed I/I 1010100101010101100moisture is uniquely identified for 0101010100 1.60" I/I Flow (cfs) 15 0.4 Static Model 01010101010101001010101010101each sewershed, is parsimonious Rain 10101010101010010101101001110 (containing relatively in nature 10 1.49" 0.62" 0.6 10101010101010101010110010101few modeling parameters) and 1.45" 0.16" 1010100101010101100predicts the amount of antecedent 0101010100 5 0.41" 0.8 01010101010101001010101010101moisture within the sewershed as a 10101010101010010101101001110variation in the capture continuous 0 1.0 coefficient. 9/10/2001 9/17/2001 9/24/2001 10/1/2001 10/8/2001 10/15/2001 10/22/2001 10/29/2001 10101010101010101010110010101 Date 1010100101010101100 0101010100 01010101010101001010101010101 10101010101010010101101001110 10101010101010101010110010101 1010100101010101100 0101010100 01010101010101001010101010101 Orchard, Hiltz & McCliment, Inc. 10101010101010010101101001110 34000 Plymouth Road | Livonia, MI 48150 | 734.522.6711 | www.ohm-advisors.com 10101010101010101010110010101
  • 2. 010101010010101010101010100101010 01010101010101010101001010110100 i3D 11001010101010101010101011001010 The i3D AM Model is an alternative to purely physical based modeling using a procedure known as 01010100101010101100 0101010100101010 system identification. The basis of this approach is to allow measured data (in this 0101010100101010101010101010101010101 case flow, rainfall and temperature) to guide the modeling process. It does not assume that the model must adhere 010101101001110010101010101010101010 to a specific preconceived notion of the physical system, but rather arrives at a statistically relevant 1001010101010100101010101100 01010101 description based on the data alone. Accordingly, this procedure differs from purely black-box 010101010101010100101010101010101010 modeling since it returns a model that offers insight into the underlying mechanics of the system. 010101010010101101001110010101010101 This is contrary to existing methods, 101010101100101010101010010101010110 which unduly enforce a predetermined 01010101001010101010101 set of physical principles on the data 10010101010101010101010 that may or may not be present in the 01010100101011010011100 actual system. 01010101010101010101100 01010101010010101010110 The application of the i3D AM model 01010101001010101010101 results in a model that accurately 10010101010101010101010 predicts the system response variation 01010100101011010011100 to antecedent moisture conditions. 01010101010101010101100 This is demonstrated in the figure i3D MODel 01010101010010101010110 below that depicts the output from the AM model in red. Note that a single model accurately 010101010010101010101010100101010 predicts both the first storm that occurred on dry AM conditions and the largest response that 01010101010101010101001010110100 occurred on wet AM conditions. The model predicts the variations in capture coefficients for the 11001010101010101010101011001010 entire simulation with no additional input or adjustment by the user. 01010100101010101100 01010101001010101 10101010010101010101010101010101010100 01011010011100101010101010101010101100 Antecedent Moisture Model Results from M2 in Garden City i3D AM MODel fiT 010101010100101010101100 0101010100101 25 0.0 10101010101001010101010101010101010101 i3D Antecedent Moisture Model was 1.16" 10010101101001110010101010101010101010 20 developed by1001010101010100101010101100 010101010 Robert S. Czachorski, 0.2 Rain (inches per hour) Observed I/I 1.60" P.E., P.H., an associate with Orchard, 10101010101010100101010101010101010101 I/I Flow (cfs) Hiltz & McCliment, Inc, in partnership 15 0.4 Antecedent Moisture Model 10101001010110100111001010101010101010 Rain with Tobin Van Pelt, Ph.D., of i3D 01011001010101010100101010101100 01010 10 1.49" 0.6 1.45" Technologies,0100101010101010101001010101010101010 0.62" LLC. i3D is based on 0.16" 5 0.41" system identification theory, using 0101010101001010110100111001010101010 0.8 techniques from the fields of signal 0101010101100101010101010010101010110 0 processing, control systems and 01010101001010101010101010010101 1.0 9/10/2001 9/17/2001 9/24/2001 Date 10/1/2001 10/8/2001 time series analysis from aerospace 10/15/2001 10/22/2001 10/29/2001 101010101010101010101001010110100 engineering. 11001010101010101010101011001010 HOw i3D wOrks 01010100101010101100 01010101001010101 10101010010101010101010101010101010100 Fast and Slow Responses Shape 01011010011100101010101010101010101100 Volume 010101010100101010101100 0101010100101 10101010101001010101010101010101010101 10010101101001110010101010101010101010 1001010101010100101010101100 010101010 10101010101010100101010101010101010101 10101001010110100111001010101010101010 01011001010101010100101010101100 01010 0100101010101010101001010101010101010  Fast Response = Inflow  Shape not predetermined  0101010101001010110100111001010101010 Volume varies based on antecedent moisture  Slow Response = Infiltration  Shape identified based on data  Variation developed based on data  Shape changes based on antecedent moisture 0101010101100101010101010010101010110 010101010010101010101010100101010 01010101010101010101001010110100 11001010101010101010101011001010

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