Thursday, January 22, 2009

Theta Implicit Weighting Factor

Written by Chris Goodell, P.E., D. WRE | WEST Consultants
Copyright © 2009. All rights reserved.

The Theta Implicit Weighting Factor is used in unsteady flow HEC-RAS as a means for providing numerical stability through the imiplicit solution of the St. Venant Equations. Without going into the details, a value of 1 for Theta provides the most stability, but sacrifices some accuracy. A value of 0.6 provides the most accuracy, but is very difficult to stabilize. So...what should we use for our unsteady flow models. There is some disagreement out there among users of HEC-RAS, but here is my take: The manual, and the class that HEC holds suggests working with a Theta value of 1.0, then when your model is stabilized, reduce it as close to 0.6 as possible. In my experience, moderate to complex models never are able to maintain stability with Theta less than around 0.8. At some point in the past, I realized that most of the time, reducing the Theta value did not produce significantly different results. However, many modelers insist that Theta should be reduced. I can't disagree with that. In principle, I believe this is correct. However, in practice, my experience shows that it makes very little difference.

I think this would make a great topic for a paper, and the research would be easy to conduct. Does anyone have any thoughts on this topic?


  1. Hello. Thank you for sharing this post. It is mind opening even 7 years later. I am currently working on a study that actually consists on very dynamic process. There are 74 different indicators to determine the selected city's development level. Methodologically my study refers to previously conducted study on the same subject. Therefore, in weighting these indicators, authors of the study that I refer have used factor 1. However, according to them, there is an implicit weighting depending on the number of indictors within a group of indicators defining the factor value or the value of a key field’s characteristic. Now, I am so complicated about the future of my study. In your opinion, in which way I should follow? Thank you!

    1. I suggest the same as the manual. Build your model with Theta = 1. Once you have a nice stable model with good results, try to reduce your theta value towards 0.6, as close as you can. Always compare the results as you do this.