Identifying Instability in SWMM5, InfoDrainage, and ICM SWMM Models

Identifying Instability in SWMM5, InfoDrainage, and ICM SWMM Models

Numerical instability is a common issue in hydraulic modeling that can lead to inaccurate or unreliable results. Fortunately, SWMM5, InfoDrainage, and ICM SWMM provide tools to help you identify and address such problems. One key indicator of potential instability lies in metrics related to flow oscillations or fluctuations within the model, though the specific name and presentation might vary slightly between the software packages.

Understanding Flow Oscillations and Instability

The core concept across all three platforms is the identification of "flow turns" or rapid changes in the direction of flow change within a link (conduit or channel). These oscillations can indicate numerical instability.

How Flow Turns (or Equivalent Metrics) are Calculated

The general process, which is conceptually similar across SWMM5, InfoDrainage, and ICM SWMM, involves these steps:

1. DQ (Flow Difference): At each time step, the model calculates the difference between the new flow (Q_new) and the old flow (Q_old) in a link. This is often referred to as DQ (DQ = Q_new - Q_old).

2. Significant Change Threshold: To filter out very small, insignificant fluctuations, a threshold is applied. A flow change is only considered if the absolute value of DQ is greater than a predefined small value (e.g., 0.001 cfs in SWMM5).

3. Sign Change: The most crucial step is checking for a change in the sign of DQ between consecutive time steps. A flow turn (or equivalent instability indicator) is counted only when the sign of DQ changes from positive to negative or from negative to positive. This signifies an oscillation – the flow rate was increasing and is now decreasing, or vice versa. It is not the same as the sign of the flow.

   • Example: If DQ was +0.05 cfs at the previous time step and is now -0.02 cfs, a flow turn is counted because the sign changed from positive to negative.
   • Monotonic Flow: If the flow is consistently increasing (DQ is always positive) or consistently decreasing (DQ is always negative), no flow turns are counted, even if the flow rate changes significantly.

Interpreting Instability Indicators

• SWMM5: SWMM5 reports a "Flow Instability Index" in the output report file (RPT file). This index lists the links with the highest number of flow turns.
• InfoDrainage: InfoDrainage provides a "Continuity Error" and other stability-related metrics in its output. You may also need to visually inspect flow hydrographs to assess stability.
• ICM SWMM: ICM SWMM offers detailed simulation logs and allows you to track flow oscillations and identify areas of instability. You can also generate reports that highlight potential stability issues. The flow instability index is called the Number of Flow Turns in ICM and the Flow Turns are listed in the Node Summary Table of the node summary csv file.

General Workflow for Assessing Instability:

1. Check Output Reports/Logs: Examine the output reports or logs generated by your chosen software. Look for sections related to flow instability, continuity errors, or warnings about oscillations.

2. Focus on Problem Areas: Identify the links (or nodes in some cases) that are flagged as having the highest instability or the most flow turns.

3. Visual Inspection: The most important step is to visually inspect the flow hydrograph for the identified links. Plot flow versus time to reveal the nature of any oscillations.

   • Stable Oscillations: Small, rapid oscillations around a relatively stable average flow might not be significant and can often be ignored. This is especially true at the beginning of the simulation before flow becomes connected.
   • Unstable Oscillations: Large, erratic spikes or fluctuations indicate significant instability that needs to be addressed.

Addressing Instability

If you find significant instability, you'll need to take corrective action. Common strategies include:

• Reducing the Time Step: Using a smaller computational time step often improves stability.
• Checking Model Input Data: Ensure that your input data (conduit geometry, roughness, boundary conditions, etc.) is accurate and free of errors.
• Adjusting Routing Method: Experiment with different routing methods (e.g., dynamic wave, kinematic wave, diffusion wave) if available in your software.
• Simplifying the Model: Sometimes, simplifying overly complex parts of the model can help.
• Software-Specific Settings: Investigate any software-specific settings related to numerical stability or damping (InfoDrainage and ICM SWMM, for example, offer under-relaxation or damping options).

Key Takeaways

• Flow oscillations, or rapid changes in flow direction, can indicate model instability.
• SWMM5, InfoDrainage, and ICM SWMM provide tools to help you identify and analyze these oscillations, although the exact terminology and presentation may differ.
• Visual inspection of flow hydrographs is crucial to determine the significance of any flagged instability.
• Addressing instability often requires adjustments to model parameters, input data, simulation settings, or the use of flow damping options in the software.

By carefully analyzing the available instability indicators and examining flow hydrographs, you can ensure the reliability and accuracy of your hydraulic model results in SWMM5, InfoDrainage, or ICM SWMM.

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.