tag:blogger.com,1999:blog-1367053740188758246.post7515094536543399221..comments2023-06-21T00:39:34.443-07:00Comments on Dosbat: Long Tail or Fast Crash?Chris Reynoldshttp://www.blogger.com/profile/16843133350978717556noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-1367053740188758246.post-7155470210883985952013-05-29T13:14:31.031-07:002013-05-29T13:14:31.031-07:00I'm pondering throwing this problem at a very ...I'm pondering throwing this problem at a very smart person. I never got round to pursuing this further. Frankly at the moment I'm not able to move this forward.Chris Reynoldshttps://www.blogger.com/profile/16843133350978717556noreply@blogger.comtag:blogger.com,1999:blog-1367053740188758246.post-11518648614926661492013-04-10T11:13:28.192-07:002013-04-10T11:13:28.192-07:00Crandles,
As it says in the post, a quadratic was...Crandles,<br /><br />As it says in the post, a quadratic was chosen to maximise R2. An exponential gives:<br /><br />Y=20.36*Exp(-0.055X)<br /><br />Where X is the previous year's minimum area. <br /><br />This has an R2 of 0.5622, and is closer to linear (as can be appreciated from the 0.055), where a linear an R2 of 0.5752.<br /><br />However having been pondering the matter I cannot see a reason to expect a strongly non linear ice growth in response to area of preceding season's. Geometry suggests this should be linear. The open water at the end of the season is merely replaced by new ice of thermodynamic equilibrium thickness ~2m.<br /><br />When I put the linear equation into the toy I get a rapid crash to zero, with a negligible tail due to constraining minimum volume to > zero. Because the quadratic ice growth counters the losses more actively as volume/area decreases, this extends the crash to minimum until year 21 or so, in the case of a linear ice growth response the ice crashes out rapidly to zero by year 17.<br /><br />This makes me happier because a fast crash would be more exciting than a drawn out tail.<br /><br />I'll blog on this tomorrow.Chris Reynoldshttps://www.blogger.com/profile/16843133350978717556noreply@blogger.comtag:blogger.com,1999:blog-1367053740188758246.post-26386445432898384912013-04-09T11:20:32.163-07:002013-04-09T11:20:32.163-07:00>"I'm still not convinced I understand...>"I'm still not convinced I understand why figure two's fit curve has the form it has, i.e. I can't off the top of my head knock together an equation based on the physics that reproduces that curve."<br /><br />Just a guess without much examination:<br />Is it the case that you have two quadratics? Adding (or subtracting) should just give a quadratic. However I suspect you have a quadratic in max volume and a quadratic in min volume. If they moved together in a 1:1 motion they would still be two quadratics but because they don't move at same speed it is two quadratics in different variables and that can give that bump.<br /><br />I expect that using exponential rather than quadratic would give much better fit to the data.crandleshttps://www.blogger.com/profile/15181530527401007161noreply@blogger.comtag:blogger.com,1999:blog-1367053740188758246.post-44418863783908576552013-04-09T10:21:25.725-07:002013-04-09T10:21:25.725-07:00Crandles,
It's occurred to me that volume lev...Crandles,<br /><br />It's occurred to me that volume levelling out at around 20k km^3 may have a physical basis: the Arctic ocean is around 10M km^2 area of ice at the start of June, when the melt begins within the ocean. If all the ice outside that region, roughly north of 70degN, is thinner adding far less volume, then most of the peak volume comes from (average) 2m thick 10M km^2 area thermodynamically thickened ice with a volume of 20k km^3.<br /><br />So 20k km^3 represents a floor until winter warming changes the game for thermodynamic thickening.<br /><br />I've been unable to get to the bottom of why the 'model' drops to zero so much more rapidly than PIOMAS is doing, guestimate - around twice as fast. One factor may be that the curves in figures 1 and 2 are dominated by the recent drop off and may not be giving due weight to the past longer 'lingering' of ice, accelerating progression along the curves faster than has happened in reality.<br /><br />I've avoided trying a more physical approach as just using fits derived from observations covers all sorts of factors. Although of course I have shaped the behaviour by my choice of what to fit to and the overall partitioning of the year.<br /><br />A problem I have with introducing base level factors like thermodynamic thickening in terms of the physics is the complexity it introduces. Although maybe I'm wrong in this.<br /><br />I'm still not convinced I understand why figure two's fit curve has the form it has, i.e. I can't off the top of my head knock together an equation based on the physics that reproduces that curve.Chris Reynoldshttps://www.blogger.com/profile/16843133350978717556noreply@blogger.comtag:blogger.com,1999:blog-1367053740188758246.post-73269568896162879132013-04-08T15:47:19.578-07:002013-04-08T15:47:19.578-07:00I decided on modeling the max volume rather than t...I decided on modeling the max volume rather than the volume gain. I suggest volume gain in winter doesn't really depend on the minimum it starts from it just approaches a thermodynamic equilibrium. The main components determining the thermodynamic equilibrium, I suggest are GHG level which keep increasing (rather linearly) and upward heat flux.<br /><br />Is that more physically plausible? if so, the bump in max volume looks odd to me. Is that due to use of quadratic fits or volume at min getting near to 0 or something else?crandleshttps://www.blogger.com/profile/15181530527401007161noreply@blogger.comtag:blogger.com,1999:blog-1367053740188758246.post-87211936042076456192013-04-08T15:38:21.238-07:002013-04-08T15:38:21.238-07:00Hi Chris,
This is very similar to what I was tryi...Hi Chris,<br /><br />This is very similar to what I was trying to do but I was trying to call it a physically based extrapolation.<br /><br />If you have the volume loss dependant on volume, isn't it logical that the increase in volume loss should be exponential rather than quadratic?<br /><br />If your model is all based on fits, it seems odd that it is so far out. I am trying to take a look at why but that might take some time.crandleshttps://www.blogger.com/profile/15181530527401007161noreply@blogger.com