Imagine you are building your dream house on a lake. To protect your investment from flooding, you hire an engineer to tell you how high up the bank to build your home and design the sea wall.
He determines which design wave height to use to protect your home, then takes that wave height and superimposes it on the record high lake level, just to be safe. When you see the results, you are surprised at how high and how expensive your sea wall must be. You are also unhappy at how high the home is above the water, hurting your view and your investment.
Wouldn’t it be nice if your engineer could tell you the chances of maximum wave height and maximum lake level happening simultaneously, or happening at all? If the chances are slim, is it worth the extra money to prevent flooding at this high elevation?
A similar scenario exists with the design of wet-weather upgrades in sewer systems. Peak wet-weather flows in sewers depend on both the magnitude of the rainfall and how wet the soil conditions are during the rain event.
While the response to rainfall is studied extensively, the effects of the antecedent moisture (AM) conditions are often ignored or oversimplified. This can lead to playing it safe by superimposing a very large design rainfall onto a very wet AM condition to model design peak flows. This results in planning upgrades that are very costly, for flows that will occur very rarely.
Now there is good news. An engineer can tell you the statistical chances of your design capacity being exceeded. Advanced technology that can accurately describe and predict the effects of AM conditions, combined with a frequency analysis of peak flows, reduces design uncertainty. This leads to higher confidence in the results and often significantly lower capital improvement costs.
As seasons change or as rain falls on a sewershed, the inflow and infiltration (I&I) entering the collection system can vary greatly. The water table will rise in spring, and the moisture content of the spongelike soils will increase as rains fall, then dry between events. You can easily see this pattern by reviewing flow monitoring data collected for the same sewershed during different times of year (Figure 1).
Due to the relative wetness of the soil, the spring rain was not absorbed by the porous soil, as it was for the summertime event, since in spring the pores were already filled with groundwater and rainfall. The water has nowhere to go except through the cracks and leaking joints of the collection system.
Standard modeling procedures involve calibrating an I&I model to actual storm events and using the resulting model to simulate a design storm. This generates very different answers depending on which storm is used for calibration (Figure 2). Assume the design event is a 10-year, 24-hour storm, and we are concerned with volume above 3 cubic feet per second to design a storage tank.
The peak flow generated by the spring storm design is almost three times higher than that of the summer storm design, and the volume generated is more than 53 times higher. There are two flaws with using this design storm approach.
First, as shown by this example, it does not account for varying AM conditions. Second, a design storm is a fictitious event that may or may not represent the wet-weather behavior of the collection system. It is better to understand the impacts of AM, as well as the wet-weather behavior of the system using actual long-term data instead of a fictitious event that may never really occur.
Constantly varying AM
Figure 3 demonstrates the impact of AM effects on several back-to-back storms. Note that while the rain volumes and intensities are similar, the flow response gets larger and larger with subsequent events. This increase in flow response is due not only to an increase in the base groundwater flow but also to an increase in rainfall-dependent I&I.
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The wetness conditions are constantly changing. To simulate this properly, a model must be able to change continuously, as well. Understanding these AM effects is critical for understanding wet-weather flows and designing system upgrades.
A new modeling technique resolves these challenges by using a widely accepted system identification theory from the aerospace industry. Unlike standard models used for hydrologic evaluation, the model is specifically tailored for each sewershed, contains a simplified set of modeling parameters, and accurately predicts the amount of AM within the sewershed by simulating a continuously varying capture coefficient.
Figure 4 depicts the workings of the AM model, generated using H2OMetrics software from i3D Technologies. Wetness conditions are tracked in the Sewershed Moisture Retention block. The model continuously adjusts the inflow, infiltration and groundwater hydrographs based on this wetness. This results in a more accurate prediction of system flows, as shown in Figure 5.
Rather than using a fictitious design storm approach, industry trends have moved toward a statistical frequency analysis, based on actual long-term data. A frequency analysis is developed by routing a long period of rainfall and temperature data through the AM model and then performing a statistical analysis on the resulting model output. Long-term flow monitoring data is not required.
This accurately represents the system flow response because it incorporates the statistical variations of both rainfall from the long-term record and antecedent moisture variations from the AM model. An example of a frequency analysis is shown in Figure 6.
This approach eliminates the problem of over-estimating flow by having to select a design rainfall event for a singular wetness condition. Because frequency analysis performs statistics on the entire range of storm events included in the long-term record, one single design storm does not have to be selected.
The engineer can now share with the decision-makers the real relationship between risks and costs. This gives decision-makers a strong basis for selecting which costs and risks they are willing to accept. It contrasts with traditional techniques in which the modeler alone incorporates the risk decisions into the model calibration by selecting specific wetness conditions.
More confidence, less cost
Standard, accepted hydrologic modeling techniques do not effectively account for the effects of AM. This inaccuracy can lead to using overly conservative modeling practices to account for the uncertainty. Using new modeling techniques along with a frequency-based design approach reduces model uncertainty, leading to higher confidence in results and significantly lower capital improvement costs. F
About the Authors
Robert Czachorski, P.E., is co-founder of i3D Technologies, a modeling and analytics software company based in Ann Arbor, Mich. (www.H2Ometrics.com). Rhonda Harris, P.E., is director of engineering services for the Columbus, Ohio, office of Orchard, Hiltz & McCliment (www.ohm-advisors.com).