Hysteresis Effect in SWMM 5's Link Flow vs. Depth Relationship

Hysteresis Effect in SWMM 5's Link Flow vs. Depth Relationship

In SWMM 5 (Storm Water Management Model), you might observe a phenomenon called hysteresis when examining the relationship between flow and depth in a channel or pipe (also known as a link). Hysteresis, in this context, means that the flow rate for a given depth is different depending on whether the water level is rising or falling. This creates a loop or "hysteresis loop" when you plot flow against depth.

Why Does Hysteresis Occur in SWMM 5?

SWMM 5 uses the full Saint-Venant equations (also referred to as the dynamic wave equations) to simulate unsteady, non-uniform flow in open channels and closed conduits. These equations account for various factors, including:

• Upstream and Downstream Water Levels (Head): The difference in water levels influences the driving force for flow.
• Hydraulic Radius: This represents the efficiency of the channel's cross-section in carrying water. It changes with depth.
• Cross-Sectional Area: The area of the flow cross-section also changes with depth, directly affecting flow capacity.
• Local and Convective Acceleration The change in velocity with respect to time and distance, respectively.

During a storm event, as the water level rises (the rising limb of the hydrograph), these factors interact in a specific way. When the water level falls (the falling limb), the combination of these factors, particularly due to the differences in flow velocity (and the local and convective acceleration), results in a different flow rate for the same depth compared to the rising limb. These different interactions create the hysteresis effect.

Factors that Influence the Magnitude of Hysteresis Several hydraulic conditions contribute to the magnitude of the hysteresis effect in SWMM 5:

1. Channel geometry Irregular or complex cross-sections can lead to more significant hysteresis.
2. Steep slopes Steeper channels often exhibit more pronounced hysteresis loops.
3. Rapidly changing flow Significant hysteresis is commonly observed during rapidly rising or falling water levels, such as during intense storms or sudden flow changes.
4. Backwater effects Downstream conditions that create backwater, like constrictions or tidal influences, significantly affect the flow-depth relationship and can increase hysteresis.

Implications of Hysteresis

• Rating Curve Inaccuracy: Hysteresis makes it impossible to create a simple rating curve that uniquely defines flow based solely on depth.
• Model Calibration: It's important to consider hysteresis during model calibration. If observed data shows hysteresis, a well-calibrated model should reproduce it.
• Result Interpretation: When analyzing SWMM 5 results, understand that a single depth value doesn't correspond to a unique flow. You must also consider whether the depth is on the rising or falling limb of the hydrograph.

Simplification and Hysteresis

It's important to note that using simplified routing methods in SWMM 5, such as the kinematic wave or diffusion wave options, will reduce or eliminate hysteresis. However, these simplifications might not be suitable for all situations, as they neglect certain terms in the Saint-Venant equations. The full dynamic wave method provides the most accurate representation of flow but also leads to the hysteresis effect in cases of rapidly varied flow. The presence of hysteresis in your results is an indication that the full dynamic wave equations are necessary to accurately simulate the flow.

Summary

Hysteresis in SWMM 5 is a real phenomenon resulting from the complex interactions captured by the full Saint-Venant equations. Recognizing and understanding this effect is crucial for accurately interpreting model results and making informed decisions based on SWMM 5 simulations. A hysteresis effect is a normal and expected result of using the full St. Venant or Dynamic Wave flow routing in SWMM 5.