1. DES 606 : Watershed Modeling with HEC-HMS
Module 13
Theodore G. Cleveland, Ph.D., P.E
26-28 August 2015

2. Channel Routing
Example 5 illustrated lag-routing for simplistic channel routing.
Lag routing does not attenuate nor change shape of the hydrograph
Conflicting arguments on where applicable
probably adequate for hydrographs that stay in a channel (no floodway involvement) and travel distance is short (couple miles).
Other methods are required where attenuation and shape change is important

3. Channel Routing
Methods that attenuate and change shape of hydrographs in HMS include
Storage
a type of level pool routing
Muskingum
a type of storage routing that accounts for wedge (non-level pool) storage
Kinematic
A type of lag routing where the lag is related to channel slopes and accumulated reach storage – considered a hydraulic technique

4. Channel Routing Consider each individually using an example
Develop required input tables
Enter into HMS
Examine results

5. Channel Routing
Channel storage routing is essentially an adaptation of level pool reservoir routing
Principal difference is how the storage and discharge tabulations are formed.
In its simplest form, the channel is treated as a level pool reservoir.

6. Channel Routing
The storage in a reach can be estimated as the product of the average cross sectional area for a given discharge rate and the reach length.

7. Channel Routing
A rating equation is used at each cross section to determine the cross section areas.

8. Channel Routing
A known inflow hydrograph and initial storage condition can be propagated forward in time to estimate the outflow hydrograph.
The choice of Dt value should be made so that it is smaller than the travel time in the reach at the largest likely flow and smaller than about 1/5 the time to peak of the inflow hydrograph
HMS is supposed to manage this issue internally

9. Channel Routing Example
Consider a channel that is 2500 feet long, with slope of 0.09%, clean sides with straight banks and no rifts or deep pools. Manning’s n is

10. Channel Routing Example
The inflow hydrograph is triangular with a time base of 3 hours, and time-to-peak of 1 hour. The peak inflow rate is 360 cfs.

11. Channel Routing Example
Configuration:
Input hydrograph
Routing Model
Output hydrograph
Q(t) t

12. Channel Routing Example
Data preparation
Construct a depth-storage-discharge table
Construct an input hydrograph table
HMS
Import the hydrograph and the routing table information
Simulate response

13. Depth-Storage Compute using cross sectional geometry
Save as depth-area table (need later for hydraulics computations)
Multiply by reach length for depth-storage
Depth
Length A4 A3 A2 A1 A1
Area
A1+A2
A1+A2+A3

14. Depth-Perimeter Compute using cross sectional geometry
Save as depth-perimeter table (need later for hydraulics computations)
Depth
Length W4 W3 W2 W1
Wetted Perimeter W1 W2 W3

15. Depth-Discharge
Compute using Manning’s equation and the topographic slope

16. Inflow Hydrograph
Create from the triangular input sketch

17. HEC-HMS
Create a generic model, use as many null elements as practical (to isolate the routing component)

18. HEC-HMS Storage-Discharge Table (from the spreadsheet)
Note the units of storage

19. HEC-HMS Meterological Model (HMS needs, but won’t use this module)
Null meterological model

20. HEC-HMS
Set control specifications, time windows, run manager – simulate response
Observe the lag from input to output and the attenuated peak from in-channel storage

21. HEC-HMS
Set control specifications, time windows, run manager – simulate response
Lag about 20 minutes
Attenuation (of the peak) is about 45 cfs
Average speed of flow about 2 ft/sec
Observe the lag from input to output and the attenuated peak from in-channel storage

22. Muskingum Routing
A variation of storage routing that accounts for wedge storage
Muskingum
Muskingum-Cunge
Level-pool Q
Inflow
Depth-Up
Wedge storage
Kinematic Wave
Outflow
Depth-Down

23. Muskingum routing is a storage-routing technique that is used to:
translate and attenuate hydrographs in natural and engineered channels
avoids the added complexity of hydraulic routing.
The method is appropriate for a stream reach that has approximately constant geometric properties.

24. At the upstream end, the inflow and storage are assumed to be related to depth by power-law models

25. At the downstream end, the outflow and storage are also assumed to be related to depth by power-law models

26. Next the depths at each end are rewritten in terms of the power law constants and the inflows

27. The weight, w, ranges between 0 and 0.5.
Then one conjectures that the storage within the reach is some weighted combination of the section storage at each end (weighted average)
The weight, w, ranges between 0 and 0.5.
When w = 0, the storage in the reach is entirely explained at the outlet end (like a level pool)
When w = 0.5, the storage is an arithmetic mean of the section storage at each end.

28. Generally the variables from the power law models are substituted
And the routing model is expressed as
z is usually assumed to be unity resulting in the usual from

29. Generally the variables from the power law models are substituted
And the routing model is expressed as
z is usually assumed to be unity resulting in the usual from

30. For most natural channels w ranges between 0. 1 and 0
For most natural channels w ranges between 0.1 and 0.3 and are usually determined by calibration studies
Muskingum-Cunge further refines the model to account for changes in the weights during computation (better reflect wedge storage changes)

31. In HEC-HMS Use same example conditions
From hydrologic literature (Haan, Barfield, Hayes) a rule of thumb for estimating w and K is
Estimate celerity from bankful discharge (or deepest discharge value)
Estimate K as ratio of reach length to celerity (units of time, essentially a reach travel time)
Estimate weight (w) as

32. In HEC-HMS
Use same example conditions

33. In HEC-HMS Use same example conditions Muskingum Parameters
Results a bit different but close
Difference is anticipated

34. In HEC-HMS Change w to 0.0, K=20 minutes, NReach=2 Level Pool
Muskingum Parameters
Results almost same as level-pool model

35. In HEC-HMS Change w to 0.5, K=20 minutes, NReach=2 Lag Routing
Muskingum Parameters
20 minute lag routing

36. Muskingum-Cunge More complicated; almost a hydraulic model
Data needs are
Cross section geometry (as paired-data)
Manning’s n in channel, left and right overbank
Slope
Reach length
Will illustrate data entry using the same example

37. Muskingum-Cunge
Cross section geometry
“Glass walls”

38. Muskingum-Cunge Associate the section with the routing element
Other data included

39. Muskingum-Cunge
Run the simulation
Result comparable to level-pool.

40. Summary Examined channel routing using three methods
Level pool routing (Puls)
Muskingum
Muskingum-Cunge
Selection of Muskingum weights allows analyst to adjust between level-pool and lag routing by changing the weighting parameter
All require external (to HMS) data preparation
Muskingum-Cunge hydraulically “familiar)

41. Summary
Parameter estimation for Muskingum method requires examination of literature external to HMS user manuals
Instructor preferences for routing
Lag routing (if can justify)
Level-pool
Muskingum-Cunge (as implemented in HMS) – very “hydraulic”
Muskingum (I would only choose if had calibration data)
Kinematic-wave