Regression Analysis For Civil Engineer -1

Let’s dive into a numerical example of a rainfall-runoff model using the S-Curve Unit Hydrograph method for a hypothetical catchment. Remember, this is a simplified illustration, but it captures the essential steps.

Example: Rainfall-Runoff Modeling for Catchment X

1. Catchment Information:

   • Catchment area (A): 10 square kilometers.
   • Time of concentration (Tc): 3 hours (time taken for runoff to reach the outlet).

2. Rainfall Data:

   • Assume we have hourly rainfall data for a storm event:
     • Hour 1: 10 mm
     • Hour 2: 20 mm
     • Hour 3: 30 mm
     • Hour 4: 15 mm
     • Hour 5: 5 mm

3. S-Curve Unit Hydrograph Parameters:

   • Time to peak (Tp): 2 hours (peak flow occurs 2 hours after the start of the storm).
   • Hydrograph duration (D): 4 hours (from the start of rainfall to the end).

4. Calculate Excess Rainfall (Rex):

   • Rex = Total rainfall - Infiltration
   • Total rainfall = 10 + 20 + 30 + 15 + 5 = 80 mm
   • Assume infiltration is negligible for this example (for simplicity).
   • Rex = 80 mm

5. S-Curve Unit Hydrograph:

   • The S-Curve unit hydrograph has a rising limb (S-curve) and a falling limb.
   • We’ll assume a triangular shape with a peak flow at Tp (2 hours) and zero flow at the start and end.

6. Calculate Hydrograph Values:

   • At each hour, calculate the flow contribution:
     • Hour 1: Flow = 0 (before the storm)
     • Hour 2 (Tp): Flow = (Rex / D) * (2 - 1) = (80 / 4) * 1 = 20 mm/hour
     • Hour 3: Flow = (Rex / D) * (3 - 1) = (80 / 4) * 2 = 40 mm/hour
     • Hour 4: Flow = (Rex / D) * (4 - 1) = (80 / 4) * 3 = 60 mm/hour
     • Hour 5: Flow = 0 (after the storm)

7. Streamflow Hydrograph:

   • Combine the flow contributions to create the streamflow hydrograph:
     • Hour 1: 0 mm/hour
     • Hour 2: 20 mm/hour
     • Hour 3: 40 mm/hour
     • Hour 4: 60 mm/hour
     • Hour 5: 0 mm/hour

8. Graphical Representation:

   • Plot the hydrograph with time (hours) on the x-axis and flow (mm/hour) on the y-axis.

Result:

The resulting streamflow hydrograph represents the flow at the outlet of Catchment X during the storm event. In practice, more complex models consider additional factors, but this example demonstrates the basic principles of rainfall-runoff modeling.

Remember that real-world applications involve calibration, validation, and consideration of spatial variability. Engineers use such models for flood prediction, water resource management, and environmental impact assessment. 🌧️🏞️