Hi,
Is this good SD practice?
Here is the background. Consider a case where wave elevation occurs in shallow water. We know that any wave builds in heights as it approaches the shoreline. That means there is a nonlinear effect of water depth on wave height: wave height increases as water depth decreases.
To model this phenomenon, I use table function to control potential wave height for each depth. Then, the potential wave height is smoothed using a smooth function. I do not use a delay function although the wave height is material, not information in nature. My formulation can be simplified as follows:
water depth--->effect of depth on wave height--->potential wave height--->[wave height]<----elevation time
The key equation is:
wave height=SMOOTHn(potential wave height, elevation time).
Is this a good expression? Notice that my model is not intended to predict the wave height, but to see its effect on other factors.
Monte
Using smooth function
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bob@vensim.com
- Senior Member
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- Joined: Wed Mar 12, 2003 2:46 pm
Hi Monte,
Determining what a wave will really look like is a messy business, but your approximation seems to be a reasonable one as long as you are trying to determine not the height of the wave, but the average peak height at a depth.
But given this I do not understand why depth would change over time - perhaps you are tracking the position of a boat or swimmer on the water. The smooth function is not appropriate in this case - all that matters is the position.
Determining what a wave will really look like is a messy business, but your approximation seems to be a reasonable one as long as you are trying to determine not the height of the wave, but the average peak height at a depth.
But given this I do not understand why depth would change over time - perhaps you are tracking the position of a boat or swimmer on the water. The smooth function is not appropriate in this case - all that matters is the position.
Hi JJ and Bob,
I try to track the position of the leading crest in a wave train. The crest's speed is solely determined by the local depth (bathymetric profile) along the propagation path. And the depth changes as the crest moves forward. So, I have a level variable called 'distance traveled' which is increased by wave speed. The speed varies as depth changes. The change in depth is due to the change in distance traveled.
Once the wave crosses the continental shelf, its height increases due to bottom friction. The wave height, then, becomes another factor determining the wave speed:
wave speed = square root (g*(d+H))
where g is gravity; d is still water depth; and H is wave height.
I try to develop a simple (highly implicit) equation for H, as a function of still water depth.
We know that the wave height will reach a maximum stable height (H_max) at a certain depth, known as breaking point, where model simulation will be stopped. We also know that 60% of wave shoaling (0.6*H_max) will occurs within the last 20 m depth.
The table function causes sudden changes in wave height, which seems to be unrealistic. So I try to make a delay explicit by using the smooth function. I am looking for a better fomulation to represent the growth in wave height, which will affects wave speed, which in turn increases distance traveled, which decreases depth, which eventually increases wave heights until it breaks as a plunging breaker.
Monte
I try to track the position of the leading crest in a wave train. The crest's speed is solely determined by the local depth (bathymetric profile) along the propagation path. And the depth changes as the crest moves forward. So, I have a level variable called 'distance traveled' which is increased by wave speed. The speed varies as depth changes. The change in depth is due to the change in distance traveled.
Once the wave crosses the continental shelf, its height increases due to bottom friction. The wave height, then, becomes another factor determining the wave speed:
wave speed = square root (g*(d+H))
where g is gravity; d is still water depth; and H is wave height.
I try to develop a simple (highly implicit) equation for H, as a function of still water depth.
We know that the wave height will reach a maximum stable height (H_max) at a certain depth, known as breaking point, where model simulation will be stopped. We also know that 60% of wave shoaling (0.6*H_max) will occurs within the last 20 m depth.
The table function causes sudden changes in wave height, which seems to be unrealistic. So I try to make a delay explicit by using the smooth function. I am looking for a better fomulation to represent the growth in wave height, which will affects wave speed, which in turn increases distance traveled, which decreases depth, which eventually increases wave heights until it breaks as a plunging breaker.
Monte
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bob@vensim.com
- Senior Member
- Posts: 1107
- Joined: Wed Mar 12, 2003 2:46 pm
Hi Monte,
It sounds like you are trying to simulate a wave by representing its average characteristics. This will not work! If you want to simulate waves there is a well defined field of study for doing this - it involved numerical solutions to partial differential equations. Vensim is absolutely not appropriate for this.
So go back and ask yourself (or tell us) why you are doing this in the first place.
It sounds like you are trying to simulate a wave by representing its average characteristics. This will not work! If you want to simulate waves there is a well defined field of study for doing this - it involved numerical solutions to partial differential equations. Vensim is absolutely not appropriate for this.
So go back and ask yourself (or tell us) why you are doing this in the first place.
Hi Bob,
I couldn't go back, although I wanted to, because I had went too far to step down.
Now, five months later, I have had my manscript, using SD for wave modeling, accepted for publication in a domain journal. I used SD for point prediction, and during validation process I had to modify a classic wave law and a classic wave theory, leading to a new method of wave exploring. I used Vensim as a key tool.
I hope this news would give you satisfaction.
Monte
I couldn't go back, although I wanted to, because I had went too far to step down.
Now, five months later, I have had my manscript, using SD for wave modeling, accepted for publication in a domain journal. I used SD for point prediction, and during validation process I had to modify a classic wave law and a classic wave theory, leading to a new method of wave exploring. I used Vensim as a key tool.
I hope this news would give you satisfaction.
Monte
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bob@vensim.com
- Senior Member
- Posts: 1107
- Joined: Wed Mar 12, 2003 2:46 pm
Hi Bob,
The paper is in English, just available online at
http://www.springerlink.com/content/g0537874x8377w53
"System dynamics" is a keyword of this paper, where Vensim equations are given in the appendix. The model is simple, with only single level and two feedback loops. Validation was done by following Forrester and Senge's classic multiple tests. The modeling process led to the modification of Green's law and solitary wave theory, which explain the dynamics of wave elevation and wave celerity, respectively.
The paper was reviewed by Dr. Tad S. Murty, Vice-President of the Tsunami Society. The reprint is being ordered by Mark, my co-author.
The paper is in English, just available online at
http://www.springerlink.com/content/g0537874x8377w53
"System dynamics" is a keyword of this paper, where Vensim equations are given in the appendix. The model is simple, with only single level and two feedback loops. Validation was done by following Forrester and Senge's classic multiple tests. The modeling process led to the modification of Green's law and solitary wave theory, which explain the dynamics of wave elevation and wave celerity, respectively.
The paper was reviewed by Dr. Tad S. Murty, Vice-President of the Tsunami Society. The reprint is being ordered by Mark, my co-author.