An advanced approach to predicting wet-weather flows in sanitary sewers that incorporates antecedent moisture effects and long-term climate data.

Introduction

Imagine that 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. He then takes that wave height and superimposes it on the record high lake level, just to be safe. When you see the final results, you are surprised at how tall, and how expensive, your sea wall must be to protect your home from these two dangers. Also, you are not happy at how high the home is above the water, minimizing your view and the potential of your investment. Wouldn’t it be nice if your engineer could tell you the chances of these two events happening simultaneously, or even happening at all? If the chances are very small, is it worth the extra money and diminished views to prevent flooding at this high elevation?

Wetness condition has a huge impact on runoff

A similar scenario exists with 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 rainfall event, just like the height of the sea wall depends on the height of the waves and the level of the lake. 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, resulting in flows that will occur very rarely, and upgrades that are very costly. But, there is good news. An engineer CAN tell you the statistical chances of your design capacity being exceeded. Advanced technology that can accurately identify and predict the effects of AM conditions, combined with a frequency analysis of peak flows, reduces uncertainty in the design. This leads to higher confidence in the results and often significantly lower capital improvement costs.

Different Responses

As seasons change or rain events fall 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 sponge like soils will increase as rains fall and then dry between events. This pattern can easily be seen by reviewing flow monitoring data collected for the same sewershed during different times of year.  

Spring & Summer Storms – Event Comparison. The I&I response of the spring storm was much larger than that of the summer storm, despite the fact that the summer rain event was much larger.

Due to the relative wetness of the soil, the rain that fell over the sewershed during the spring was not absorbed by the porous voids within the soil, as it was for the summertime event. Those voids were already filled with groundwater and rainfall in the spring. The water has nowhere else to go, except for through the cracks and leaking joints of the collection system.

Different Answers

Standard modeling procedures involve calibrating an I&I model to actual storm events and then using the resulting model to simulate a design storm. As shown in the figure below, this process generates very different answers depending on which storm is used for calibration. Let’s assume the design storm event is a 10-year, 24-hour storm, and we are concerned with volume over 3 cfs to design a storage tank.

Spring & Summer Storms – Design Storm Comparison. The modeled response for the same design rain event can vary greatly due depending on which wetness condition the model is calibrated to.

The peak flow generated by the Spring Storm design is almost 3 times higher than that of the Summer Storm design. The volume generated is more than 53 times higher. There are two flaws with using the design storm approach. Firstly, as shown by the example above, it does not account for varying AM conditions. Secondly, a design storm is a fictitious event that may or may not be representative of the wet weather behavior of the collection system. Wouldn’t it be better to understand the impacts of AM, as well as the wet weather behavior of the collection system using actual long term data rather than a fictitious event that may never really occur?

Constantly Varying AM

The figures below demonstrates the impact of AM effects on several back-to-back storms. Note that the rain volumes and intensities are similar; however 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 ground water flow but also due to an increase in rainfall dependent I&I.

Increasing antecedent moisture effect from back to back storms

The effects of back-to-back storms on AM are shown in this flow data.

 

Season antecedent moisture effects

Season antecedent moisture effects have large impacts on flows and volumes from spring to summer.

The wetness conditions are constantly changing. In order to simulate this properly, a model must be capable of changing continuously as well. Understanding these AM effects is critical for understanding wet weather flows and designing system upgrades. 

Event Models Don’t Work Very Well

Event models such as a unit hydrograph, the SCS method, or the RTK synthetic unit hydrograph are frequently used to simulate I&I in sanitary sewers. However, because these are static, linear models and do not change for varying antecedent moisture effects, they do a poor job of simulating these systems, as shown in the examples below.

Event model calibrated to the first storm. The model simply does not know that the system is getting wetter.

 

Event model calibrated to the largest flow event to be safe. The model  over-predicts all other storms, which can lead to low confidence in the model and is likely too conservative.

This leads to the dilemma of deciding which storm to use for model calibration and system design. Often, engineering judgement is used rather than scientific principles. Should we really be sizing multi-million or multi-billion dollar capital improvement based on engineering judgement?

Which storm are you going to pick?

Increasing Accuracy

The H2Ometrics AM modeling technique solves these challenges by using widely accepted system identification theory from the aerospace industry. Unlike standard models used for hydrologic evaluation, the resulting 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.

H2Ometrics Model Structure.
This figure shows a block diagram of the H2Ometrics model

The model structure above depicts how the AM model works. Wetness conditions are computed and tracked using rainfall and air temperature, which is a surrogate variable that represents other season effects in the hydrologic cycle like evaporation, evapotranspiration, ground water levels, solar radiance. etc. 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 the figures below.

Antecedent moisture model fit for back to back storms

H2Ometrics antecedent moisture model accurately predicts flow variations from back to back storms.

H2Ometrics antecedent moisture model accurately predicts flow variations from season effects.

Frequency Based Design

Rather than using a fictitious design storm approach or trying to select an appropriate wetness condition, we can use 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.

Move from design event to frequency approach.

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, just like wave height was incorporated with lake level. An example of a frequency analysis is shown below.

Frequency Analysis – This plot shows the results of the frequency analysis for existing peak flows. Using the results of the long-term simulation, the annual frequency of any flow rate can be determined from such a plot.

This approach eliminates the problem of over estimating flow caused 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 provides decision makers with a strong basis for selecting which costs and risks they are most comfortable with. This contrasts traditional techniques in which the modeler alone incorporates these risk decisions into the model calibration by selecting specific wetness conditions.

Conclusions

Standard, accepted hydrologic modeling techniques do not effectively account for the effects of AM. This inaccuracy can lead to overly conservative modeling practices in order to account for the uncertainty. Using the H2Ometrics AM model, along with a frequency based design approach, reduces this model uncertainty, leading to higher confidence in results, and significantly lower capital improvement costs.

This methodology has been used on hundreds of sewersheds across the country over the past 15 years since it was developed. 

H2Ometrics and AMM

H2Ometrics was developed specifically to aid owners and engineers in rapidly performing these types of data analytics necessary for antecedent moisture modeling. Here is a link to short overview video about the platform. Here is a link to several case studies that demonstrate how our customers are using these tools. Below are links to several tutorial videos that demonstrate many of these tools with the H2Ometrics platform.

H2Ometrics contains powerful data analytics tools for processing flow meter data.